　　

00-XX	总论		General
00-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
00-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
00Axx	一般的和各种特殊的课题		General and miscellaneous specific topics
00A05	普通数学		General mathematics
00A06	非数学家的数学(工程、社会科学等)		Mathematics for nonmathematicians (engineering, social sciences, etc.)
00A07	问题集		Problem books
00A08	趣味数学[参见97A20]		Recreational mathematics [See also 97A20]
00A09	数学普及		Popularization of mathematics
00A15	书目		Bibliographies
00A17	外国书评		External book reviews
00A20	辞典和其它一般参考书		Dictionaries and other general reference works
00A22	公式集		Formularies
00A30	数学哲学[参见03A05]		Philosophy of mathematics [See also 03A05]
00A35	数学方法论, 教学法[参见97Cxx, 97Dxx]		Methodology of mathematics, didactics [See also 97Cxx, 97Dxx]
00A65	数学和音乐		Mathematics and music
00A66	数学和视觉艺术, 可视化		Mathematics and visual arts, visualization
00A67	数学和建筑学		Mathematics and architecture
00A69	一般应用数学(物理, 见00A79和70-XX到86-XX部分)		General applied mathematics (For physics, see 00A79 and Sections 70 through 86)
00A71	数学建模理论		Theory of mathematical modeling
00A72	一般模拟方法		General methods of simulation
00A73	维数分析		Dimensional analysis
00A79	物理学(尽可能使用从70-XX到86-XX更明确的分类)		Physics (use more specific entries from Sections 70 through 86 when possible)
00A99	其它		Miscellaneous topics
00Bxx	会议录与论文集		Conference proceedings and collections of papers
00B05	演讲摘要集		Collections of abstracts of lectures
00B10	一般论文集		Collections of articles of general interest
00B15	专题论文集		Collections of articles of miscellaneous specific content
00B20	一般会议录		Proceedings of conferences of general interest
00B25	专题会议录		Proceedings of conferences of miscellaneous specific interest
00B30	纪念文集		Festschriften
00B50	精选译文集		Volumes of selected translations
00B55	其它译文合订本		Miscellaneous volumes of translations
00B60	再版文集[参见01A75]		Collections of reprinted articles [See also 01A75]
00B99	其它		None of the above, but in this section
01-XX	历史与传记[参见其它一级类目中的分类号-03部分]		History and biography [See also the classification number -03 in the other sections]
01-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
01-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
01-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
01-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
01-08	计算方法		Computational methods
01Axx	数学史和数学家		History of mathematics and mathematicians
01A05	一般历史, 原始资料集		General histories, source books
01A07	民族数学, 一般问题		Ethnomathematics, general
01A10	旧石器时代, 新石器时代		Paleolithic, Neolithic
01A12	美洲土著文化		Indigenous cultures of the Americas
01A13	其它土著文化(非欧洲)		Other indigenous cultures (non-European)
01A15	欧洲土著文化(前希腊时期等)		Indigenous European cultures (pre-Greek, etc.)
01A16	埃及		Egyptian
01A17	巴比伦		Babylonian
01A20	希腊, 罗马		Greek, Roman
01A25	中国		China
01A27	日本		Japan
01A29	东南亚		Southeast Asia
01A30	伊斯兰(中世纪)		Islam (Medieval)
01A32	印度		India
01A35	中世纪		Medieval
01A40	15, 16世纪, 文艺复兴时期		15th and 16th centuries, Renaissance
01A45	17世纪		17th century
01A50	18世纪		18th century
01A55	19世纪		19th century
01A60	20世纪		20th century
01A61	21世纪		Twenty-first century
01A65	当代的		Contemporary
01A67	未来展望		Future prospectives
01A70	传记, 讣告, 轶事, 书目		Biographies, obituaries, personalia, bibliographies
01A72	数学学派		Schools of mathematics
01A73	大学		Universities
01A74	其它研究所和大专院校		Other institutions and academies
01A75	文集或选集; 经典著作的再版或翻译[参见00B60]		Collected or selected works; reprintings or translations of classics [See also 00B60]
01A80	数学社会学(和职业)		Sociology (and profession) of mathematics
01A85	历史书目		Historiography
01A90	书目研究		Bibliographic studies
01A99	其它		Miscellaneous topics
03-XX	数理逻辑与基础		Mathematical logic and foundations
03-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
03-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
03-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
03-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
03-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
03-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
03Axx	逻辑和基础的哲学方面		Philosophical aspects of logic and foundations
03A05	哲学与评论(数学哲学, 参见00A30)		Philosophical and critical (For philosophy of mathematics, see also 00A30)
03A10	科学哲学中的逻辑		Logic in the philosophy of science
03A99	其它		None of the above, but in this section
03Bxx	一般逻辑		General logic
03B05	经典命题逻辑		Classical propositional logic
03B10	经典一阶逻辑		Classical first-order logic
03B15	高阶逻辑和类型论		Higher-order logic and type theory
03B20	经典逻辑子系统(包括直觉主义逻辑)		Subsystems of classical logic (including intuitionistic logic)
03B22	抽象演绎系统		Abstract deductive systems
03B25	理论的可判定性和命题集[参见11U05, 12L05, 20F10]		Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]
03B30	经典理论的基础(包括反演数学)[参见03F35]		Foundations of classical theories (including reverse mathematics) [See also 03F35]
03B35	证明和逻辑运算的机械化[参见68T15]		Mechanization of proofs and logical operations [See also 68T15]
03B40	组合逻辑和λ-演算[参见68N18]		Combinatory logic and lambda-calculus [See also 68N18]
03B42	知识和信仰的逻辑(包括信仰改变)		Logic of knowledge and belief (including belief change)
03B44	瞬时逻辑		Temporal logic
03B45	模态逻辑(包括标准逻辑)(知识和信仰逻辑, 见03B42; 瞬时逻辑, 见03B44; 可证明性逻辑, 参见03F45)		Modal logic (including the logic of norms) (For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45)
03B47	子结构逻辑(包括相关, 蕴涵, 线性逻辑, Lambek演算, BCK和BCI逻辑)(证明论方面, 见03F52)		Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) (For proof-theoretic aspects, see 03F52)
03B48	概率和归纳逻辑[参见60A05]		Probability and inductive logic [See also 60A05]
03B50	多值逻辑		Many-valued logic
03B52	Fuzzy逻辑; 模糊逻辑[参见68T27, 68T37, 94D05]		Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05]
03B53	仿相容逻辑		paraconsistent logics
03B55	中介逻辑		Intermediate logics
03B60	其它非经典逻辑		Other nonclassical logic
03B62	组合逻辑		Combined logics
03B65	自然语言逻辑[参见68T50, 91F20]		Logic of natural languages [See also 68T50, 91F20]
03B70	计算机科学中的逻辑[参见68-XX]		Logic in computer science [See also 68-XX]
03B80	逻辑的其它应用		Other applications of logic
03B99	其它		None of the above, but in this section
03Cxx	模型论		Model theory
03C05	等式类, 泛代数[参见08Axx, 08Bxx, 18C05]		Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05]
03C07	一阶语言和结构的基本性质		Basic properties of first-order languages and structures
03C10	量词消去, 模型完备性和有关课题		Quantifier elimination, model completeness and related topics
03C13	有限结构[参见68Q15, 68Q19]		Finite structures [See also 68Q15, 68Q19]
03C15	可数结构		Denumerable structures
03C20	超积及有关构造		Ultraproducts and related constructions
03C25	模型论力迫		Model-theoretic forcing
03C30	其它模型构造		Other model constructions
03C35	理论的范畴性和完备性		Categoricity and completeness of theories
03C40	插值, 保存, 可定义性		Interpolation, preservation, definability
03C45	分类理论, 稳定性和有关概念[参见03C48]		Classification theory, stability and related concepts [See also 03C48]
03C48	抽象元素类及有关课题[参见03C45]		Abstract elementary classes and related topics [See also 03C45]
03C50	具有特殊性质的(饱和的、刚性的等)模型		Models with special properties (saturated, rigid, etc.)
03C52	模型类的性质		Properties of classes of models
03C55	集合论模型论		Set-theoretic model theory
03C57	有效和递归论模型论[参见03D45]		Effective and recursion-theoretic model theory [See also 03D45]
03C60	模型论代数[参见08C10, 12Lxx, 13L05]		Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
03C62	算术模型与集合论模型[参见03Hxx]		Models of arithmetic and set theory [See also 03Hxx]
03C64	有序结构的模型论; o-极小性		Model theory of ordered structures; o-minimality
03C65	其它数学理论模型		Models of other mathematical theories
03C68	其它经典一阶模型论		Other classical first-order model theory
03C70	容许集上的逻辑		Logic on admissible sets
03C75	其它无穷逻辑		Other infinitary logic
03C80	有附加量词和算子的逻辑[参见03B42, 03B44, 03B45, 03B48]		Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48]
03C85	二阶和高阶模型论		Second- and higher-order model theory
03C90	非经典模型(Boole值、层等)		Nonclassical models (Boolean-valued, sheaf, etc.)
03C95	抽象模型论		Abstract model theory
03C98	模型论的应用[参见03C60]		Applications of model theory [See also 03C60]
03C99	其它		None of the above, but in this section
03Dxx	可计算性和递归论		Computability and recursion theory
03D03	Thue系统和Post系统等		Thue and Post systems, etc.
03D05	与逻辑问题有关的自动机和形式语法[参见68Q45, 68Q70, 68R15]		Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15]
03D10	Turing机和有关概念[参见68Q05]		Turing machines and related notions [See also 68Q05]
03D15	计算的复杂性(包括隐式计算复杂性)[参见68Q15, 68Q17]		Complexity of computation (including implicit computational complexity) [See also 68Q15, 68Q17]
03D20	递归函数和关系, 次递归层级		Recursive functions and relations, subrecursive hierarchies
03D25	递归(可计算)可数集和度		Recursively (computably) enumerable sets and degrees
03D28	其它Turing度结构		Other Turing degree structures
03D30	其它度和可约性		Other degrees and reducibilities
03D32	算法随机性和维数[参见68Q30]		Algorithmic randomness and dimension [See also 68Q30]
03D35	命题集的不可判定性和度		Undecidability and degrees of sets of sentences
03D40	字问题等[参见06B25, 08A50, 20F10, 68R15]		Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15]
03D45	记数法理论, 有效表述结构[参见03C57; 直觉主义及其相似的方法, 见03F55]		Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]
03D50	集合和结构的递归等价类型, 孤点元		Recursive equivalence types of sets and structures, isols
03D55	谱系		Hierarchies
03D60	次序、容许集等的可计算性和递归论		Computability and recursion theory on ordinals, admissible sets, etc.
03D65	高阶递归和集递归理论		Higher-type and set recursion theory
03D70	归纳可定义性		Inductive definability
03D75	抽象公理化可计算性和递归理论		Abstract and axiomatic computability and recursion theory
03D78	实数计算(构造性方面, 见03F60)		Computation over the reals (For constructive aspects, see 03F60)
03D80	可计算性和递归论的应用		Applications of computability and recursion theory
03D99	其它		None of the above, but in this section
03Exx	集合论		Set theory
03E02	分拆关系		Partition relations
03E04	有序集及其共尾性; pcf理论		Ordered sets and their cofinalities; pcf theory
03E05	其它组合集合论		Other combinatorial set theory
03E10	序数和基数		Ordinal and cardinal numbers
03E15	描述集合论[参见28A05, 54H05]		Descriptive set theory [See also 28A05, 54H05]
03E17	连续统的基数特征		Cardinal characteristics of the continuum
03E20	其它经典集合论(包括函数, 关系和集代数)		Other classical set theory (including functions, relations, and set algebra)
03E25	选择公理和有关命题		Axiom of choice and related propositions
03E30	经典集合论的公理体系及其若干方面		Axiomatics of classical set theory and its fragments
03E35	相容性和独立性的结果		Consistency and independence results
03E40	力迫和Boole值模型的其它方面		Other aspects of forcing and Boolean-valued models
03E45	内模型, 包括可构造性, 序数可定义性和核心模型		Inner models, including constructibility, ordinal definability, and core models
03E47	集合论可定义性的其它概念		Other notions of set-theoretic definability
03E50	连续统假设和Martin公理[参见03E57]		Continuum hypothesis and Martin’s axiom [See also 03E57]
03E55	大基数		Large cardinals
03E57	一般绝对性和力迫公理[参见03E50]		Generic absoluteness and forcing axioms [See also 03E50]
03E60	确定性原理		Determinacy principles
03E65	其它假设和公理		Other hypotheses and axioms
03E70	非经典集合论和二阶集合论		Nonclassical and second-order set theories
03E72	模糊集论		Fuzzy set theory
03E75	集合论的应用		Applications of set theory
03E99	其它		None of the above, but in this section
03Fxx	证明论和构造性数学		Proof theory and constructive mathematics
03F03	证明论, 一般问题		Proof theory, general
03F05	切割-消去法和范式定理		Cut-elimination and normal-form theorems
03F07	证明的结构		Structure of proofs
03F10	证明论中的泛函		Functionals in proof theory
03F15	递归序数和序数记号		Recursive ordinals and ordinal notations
03F20	证明的复杂性		Complexity of proofs
03F25	有关相容性和解释		Relative consistency and interpretations
03F30	一阶算术及若干方面		First-order arithmetic and fragments
03F35	二阶和高阶算术及若干方面[参见03B30]		Second- and higher-order arithmetic and fragments [See also 03B30]
03F40	Gödel编号及不完全性问题		Gödel numberings and issues of incompleteness
03F45	可证明逻辑和相关代数(例如: 可对角化代数)[参见03B45, 03G25, 06E25]		Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25]
03F50	构造系统元数学		Metamathematics of constructive systems
03F52	线性逻辑及其它子结构逻辑[参见03B47]		Linear logic and other substructural logics [See also 03B47]
03F55	直觉主义数学		Intuitionistic mathematics
03F60	构造性和递归分析[参见03B30, 03D45, 03D78, 26E40, 46S30, 47S30]		Constructive and recursive analysis [See also 03B30, 03D45, 03D78, 26E40, 46S30, 47S30]
03F65	其它构造性数学[参见03D45]		Other constructive mathematics [See also 03D45]
03F99	其它		None of the above, but in this section
03Gxx	代数逻辑		Algebraic logic
03G05	Boole代数[参见06Exx]		Boolean algebras [See also 06Exx]
03G10	格和有关结构[参见06Bxx]		Lattices and related structures [See also 06Bxx]
03G12	量子逻辑[参见06C15, 81P10]		Quantum logic [See also 06C15, 81P10]
03G15	柱型代数和多圆柱型代数; 关系代数		Cylindric and polyadic algebras; relation algebras
03G20	Łukasiewicz代数和Post代数[参见06D25, 06D30]		Łukasiewicz and Post algebras [See also 06D25, 06D30]
03G25	与逻辑有关的其它代数[参见03F45, 06D20, 06E25, 06F35]		Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
03G27	抽象代数逻辑		Abstract algebraic logic
03G30	范畴逻辑, 普遍概念[参见18B25, 18C05, 18C10]		Categorical logic, topoi [See also 18B25, 18C05, 18C10]
03G99	其它		None of the above, but in this section
03Hxx	非标准模型[参见03C62]		Nonstandard models [See also 03C62]
03H05	数学中的非标准模型[参见26E35, 28E05, 30G06, 46S20, 47S20, 54J05]		Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05]
03H10	非标准模型的其它应用(经济学、物理学等)		Other applications of nonstandard models (economics, physics, etc.)
03H15	算术的非标准模型[参见11U10, 12L15, 13L05]		Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]
03H99	其它		None of the above, but in this section
05-XX	组合学(有限域, 见11Txx)		Combinatorics (For finite fields, see 11Txx)
05-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
05-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
05-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
05-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
05-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
05-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
05Axx	枚举组合学(图论中的枚举, 见05C30)		Enumerative combinatorics (For enumeration in graph theory, see 05C30)
05A05	排列, 字, 矩阵		Permutations, words, matrices
05A10	阶乘, 二项式系数, 组合函数[参见11B65, 33Cxx]		Factorials, binomial coefficients, combinatorial functions [See also 11B65, 33Cxx]
05A15	精确枚举问题, 生成函数[参见33Cxx, 33Dxx]		Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
05A16	渐近枚举		Asymptotic enumeration
05A17	整数划分[参见11P81, 11P82, 11P83]		Partitions of integers [See also 11P81, 11P82, 11P83]
05A18	集合划分		Partitions of sets
05A19	组合恒等式, 双射组合学		Combinatorial identities, bijective combinatorics
05A20	组合不等式		Combinatorial inequalities
05A30	q-运算与有关课题[参见33Dxx]		q-calculus and related topics [See also 33Dxx]
05A40	哑运算		Umbral calculus
05A99	其它		None of the above, but in this section
05Bxx	设计与构形(设计理论的应用, 见94C30)		Designs and configurations (For applications of design theory, see 94C30)
05B05	区组设计[参见51E05, 62K10]		Block designs [See also 51E05, 62K10]
05B07	三元系		Triple systems
05B10	差集(数论、群论等)[参见11B13]		Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]
05B15	正交阵列, Latin方, Room方		Orthogonal arrays, Latin squares, Room squares
05B20	矩阵(关联阵、Hadamard阵等)		Matrices (incidence, Hadamard, etc.)
05B25	有限几何[参见51D20, 51Exx]		Finite geometries [See also 51D20, 51Exx]
05B30	其它设计, 构形[参见51E30]		Other designs, configurations [See also 51E30]
05B35	拟阵, 几何格[参见52B40, 90C27]		Matroids, geometric lattices [See also 52B40, 90C27]
05B40	填装与覆盖[参见11H31, 52C15, 52C17]		Packing and covering [See also 11H31, 52C15, 52C17]
05B45	嵌图和贴砖问题[参见52C20, 52C22]		Tessellation and tiling problems [See also 52C20, 52C22]
05B50	多米诺骨牌		Polyominoes
05B99	其它		None of the above, but in this section
05Cxx	图论(图的应用, 见68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)		Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15)
05C05	树		Trees
05C07	顶点度[参见05E30]		Vertex degrees [See also 05E30]
05C10	平面图; 图论的几何及拓扑方面[参见57M15, 57M25]		Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
05C12	图中距离		Distance in graphs
05C15	图和超图的着色		Coloring of graphs and hypergraphs
05C17	完美图		Perfect graphs
05C20	有向图, 竞赛图		Directed graphs (digraphs), tournaments
05C21	图中流		Flows in graphs
05C22	符号图和加权图		Signed and weighted graphs
05C25	图与抽象代数(群、环、域等)[参见20F65]		Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]
05C30	图论中的枚举		Enumeration in graph theory
05C31	图多项式		Graph polynomials
05C35	极图问题[参见90C35]		Extremal problems [See also 90C35]
05C38	路和圈[参见90B10]		Paths and cycles [See also 90B10]
05C40	连通性		Connectivity
05C42	密度(韧性等)		Density (toughness, etc.)
05C45	Euler图和Hamilton图		Eulerian and Hamiltonian graphs
05C50	图和线性代数(矩阵、特征值等)		Graphs and linear algebra (matrices, eigenvalues, etc.)
05C51	图设计与同构分解[参见05B30]		Graph designs and isomorphic decomposition [See also 05B30]
05C55	广义Ramsey理论[参见 05D10]		Generalized Ramsey theory [See also 05D10]
05C57	图上博弈[参见91A43, 91A46]		Games on graphs [See also 91A43, 91A46]
05C60	同构问题(重构猜想等)与同态(子图嵌入等)		Isomorphism problems (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C62	图表示(几何和相交表示等)(图形制图, 参见68R10)		Graph representations (geometric and intersection representations, etc.) (For graph drawing, see also 68R10)
05C63	无限图		Infinite graphs
05C65	超图		Hypergraphs
05C69	控制集, 独立集, 团		Dominating sets, independent sets, cliques
05C70	因子, 匹配, 划分, 覆盖和填装		Factorization, matching, partitioning, covering and packing
05C72	分数图论, 模糊图论		Fractional graph theory, fuzzy graph theory
05C75	各种图族的结构特征		Structural characterization of families of graphs
05C76	图运算(线图、积等)		Graph operations (line graphs, products, etc.)
05C78	图标号(优美图、带宽等)		Graph labelling (graceful graphs, bandwidth, etc.)
05C80	随机图[参见 60B20]		Random graphs [See also 60B20]
05C81	图上随机游动		Random walks on graphs
05C82	小世界图, 复杂网络[参见90Bxx, 91D30]		Small world graphs, complex networks [See also 90Bxx, 91D30]
05C83	图子式		Graph minors
05C85	图算法[参见68R10, 68W05]		Graph algorithms [See also 68R10, 68W05]
05C90	应用[参见68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]		Applications [See also 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15]
05C99	其它		None of the above, but in this section
05Dxx	极值组合学		Extremal combinatorics
05D05	极值集合论		Extremal set theory
05D10	Ramsey理论[参见05C55]		Ramsey theory [See also 05C55]
05D15	横截(匹配)理论		Transversal (matching) theory
05D40	概率方法		Probabilistic methods
05D99	其它		None of the above, but in this section
05Exx	代数组合学		Algebraic combinatorics
05E05	对称函数和推广		Symmetric functions and generalizations
05E10	表示理论的组合方面[参见20C30]		Combinatorial aspects of representation theory [See also 20C30]
05E15	群和代数的组合方面[参见14Nxx, 22E45, 33C80]		Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80]
05E18	组合结构上的群作用		Group actions on combinatorial structures
05E30	结合概型, 强正则图		Association schemes, strongly regular graphs
05E40	交换代数的组合方面		Combinatorial aspects of commutative algebra
05E45	单纯复形的组合方面		Combinatorial aspects of simplicial complexes
05E99	其它		None of the above, but in this section
06-XX	序, 格, 有序的代数结构[参见18B35]		Order, lattices, ordered algebraic structures [See also 18B35]
06-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
06-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
06-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
06-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
06-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
06-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
06Axx	有序集		Ordered sets
06A05	全序		Total order
06A06	偏序, 一般问题		Partial order, general
06A07	偏序集组合学		Combinatorics of partially ordered sets
06A11	偏序集的代数方面		Algebraic aspects of posets
06A12	半格[参见20M10; 拓扑半格, 见22A26]		Semilattices [See also 20M10; for topological semilattices see 22A26]
06A15	Galois对应, 闭包算子		Galois correspondences, closure operators
06A75	有序集的推广		Generalizations of ordered sets
06A99	其它		None of the above, but in this section
06Bxx	格[参见03G10]		Lattices [See also 03G10]
06B05	结构理论		Structure theory
06B10	理想, 同余关系		Ideals, congruence relations
06B15	表示理论		Representation theory
06B20	格簇		Varieties of lattices
06B23	完备格, 完备化		Complete lattices, completions
06B25	自由格, 射影格, 字问题[参见03D40, 08A50, 20F10]		Free lattices, projective lattices, word problems [See also 03D40, 08A50, 20F10]
06B30	拓扑格, 序拓扑[参见06F30, 22A26, 54F05, 54H12]		Topological lattices, order topologies [See also 06F30, 22A26, 54F05, 54H12]
06B35	连续格和偏序集, 应用[参见06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]		Continuous lattices and posets, applications [See also 06B30, 06D10, 06F30, 18B35, 22A26, 68Q55]
06B75	格的推广		Generalizations of lattices
06B99	其它		None of the above, but in this section
06Cxx	模格, 补格		Modular lattices, complemented lattices
06C05	模格, Desargues格		Modular lattices, Desarguesian lattices
06C10	半模格, 几何格		Semimodular lattices, geometric lattices
06C15	补格, 正交补格和偏序集[参见03G12, 81P10]		Complemented lattices, orthocomplemented lattices and posets [See also 03G12, 81P10]
06C20	补模格, 连续几何		Complemented modular lattices, continuous geometries
06C99	其它		None of the above, but in this section
06Dxx	分配格		Distributive lattices
06D05	结构与表示理论		Structure and representation theory
06D10	完全分配性		Complete distributivity
06D15	伪补格		Pseudocomplemented lattices
06D20	Heyting代数[参见03G25]		Heyting algebras [See also 03G25]
06D22	框架, 场所(拓扑问题见54-XX)		Frames, locales (For topological questions see 54-XX)
06D25	Post代数[参见03G20]		Post algebras [See also 03G20]
06D30	De Morgan代数, Łukasiewicz代数[参见03G20]		De Morgan algebras, Łukasiewicz algebras [See also 03G20]
06D35	MV-代数		MV-algebras
06D50	格和对偶性		Lattices and duality
06D72	Fuzzy格(软代数)和相关课题		Fuzzy lattices (soft algebras) and related topics
06D75	分配格的其它推广		Other generalizations of distributive lattices
06D99	其它		None of the above, but in this section
06Exx	Boole代数(Boole环)[参见03G05]		Boolean algebras (Boolean rings) [See also 03G05]
06E05	结构理论		Structure theory
06E10	链条件, 完备代数		Chain conditions, complete algebras
06E15	Stone空间(Boole空间)和有关构造		Stone space (Boolean spaces) and related constructions
06E20	环理论性质[参见16E50, 16G30]		Ring-theoretic properties [See also 16E50, 16G30]
06E25	有加法运算的Boole代数(可对角化代数等)[参见03G25, 03F45]		Boolean algebras with additional operations (diagonalizable algebras, etc.) [See also 03G25, 03F45]
06E30	Boole函数[参见94C10]		Boolean functions [See also 94C10]
06E75	Boole代数的推广		Generalizations of Boolean algebras
06E99	其它		None of the above, but in this section
06Fxx	有序结构		Ordered structures
06F05	有序半群和幺半群[参见20Mxx]		Ordered semigroups and monoids [See also 20Mxx]
06F07	局量子		Quantales
06F10	Noether格		Noether lattices
06F15	有序群[参见20F60]		Ordered groups [See also 20F60]
06F20	有序Abel群, Riesz群, 有序线性空间[参见46A40]		Ordered abelian groups, Riesz groups, ordered linear spaces [See also 46A40]
06F25	有序环, 有序代数, 有序模(有序域, 见12J15; 参见13J25, 16W80)		Ordered rings, algebras, modules (For ordered fields, see 12J15; see also 13J25, 16W80)
06F30	拓扑格, 序拓扑[参见06B30, 22A26, 54F05, 54H12]		Topological lattices, order topologies [See also 06B30, 22A26, 54F05, 54H12]
06F35	BCK-代数, BCI-代数[参见03G25]		BCK-algebras, BCI-algebras [See also 03G25]
06F99	其它		None of the above, but in this section
08-XX	一般代数系统		General algebraic systems
08-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
08-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
08-02	研究阐述(教著, 评述论文)		Research exposition (monographs, survey articles)
08-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
08-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
08-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
08Axx	代数结构[参见03C05]		Algebraic structures [See also 03C05]
08A02	关系系统, 合成定律		Relational systems, laws of composition
08A05	结构理论		Structure theory
08A30	子代数, 同余关系		Subalgebras, congruence relations
08A35	自同构, 自同态		Automorphisms, endomorphisms
08A40	运算, 多项式, 初等代数		Operations, polynomials, primal algebras
08A45	等价紧性		Equational compactness
08A50	字问题[参见03D40, 06B25, 20F10, 68R15]		Word problems [See also 03D40, 06B25, 20F10, 68R15]
08A55	偏代数		Partial algebras
08A60	一元代数		Unary algebras
08A62	有限代数		Finitary algebras
08A65	无限代数		Infinitary algebras
08A68	非纯一代数		Heterogeneous algebras
08A70	泛代数在计算机科学中的应用		Applications of universal algebra in computer science
08A72	Fuzzy代数结构		Fuzzy algebraic structures
08A99	其它		None of the above, but in this section
08Bxx	簇[参见03C05]		Varieties [See also 03C05]
08B05	等价逻辑, Mal'cev (Mal'tsev)条件		Equational logic, Mal'cev (Mal'tsev) conditions
08B10	同余模性, 同余分配性		Congruence modularity, congruence distributivity
08B15	簇格		Lattices of varieties
08B20	自由代数		Free algebras
08B25	积, 融和积, 各种极限和上极限[参见18A30]		Products, amalgamated products, and other kinds of limits and colimits [See also 18A30]
08B26	次直积与次直不可约性		Subdirect products and subdirect irreducibility
08B30	内射, 射影		Injectives, projectives
08B99	其它		None of the above, but in this section
08Cxx	其它代数类		Other classes of algebras
08C05	代数范畴[参见18C05]		Categories of algebras [See also 18C05]
08C10	公理化模型类[参见03Cxx, 特别见03C60]		Axiomatic model classes [See also 03Cxx, in particular 03C60]
08C15	拟簇		Quasivarieties
08C20	代数类的自然对偶性[参见06E15, 18A40, 22A30]		Natural dualities for classes of algebras [See also 06E15, 18A40, 22A30]
08C99	其它		None of the above, but in this section
11-XX	数论		Number theory
11-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
11-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
11-02	研究阐述(教著, 评述论文)		Research exposition (monographs, survey articles)
11-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
11-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
11-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
11Axx	初等数论(数域中的模拟, 见11R04)		Elementary number theory (For analogues in number fields, see 11R04)
11A05	乘法结构; Euclid算法; 最大公约数		Multiplicative structure; Euclidean algorithm; greatest common divisors
11A07	同余; 原根; 剩余系		Congruences; primitive roots; residue systems
11A15	幂剩余, 互反性		Power residues, reciprocity
11A25	算术函数; 相关数; 反演公式		Arithmetic functions; related numbers; inversion formulas
11A41	素数		Primes
11A51	因子分解; 基本性质		Factorization; primality
11A55	连分数(近似结果, 见11J70)[参见11K50, 30B70, 40A15]		Continued fractions (For approximation results, see 11J70) [See also 11K50, 30B70, 40A15]
11A63	基数表示; 数字问题(度量结果, 见11K16)		Radix representation; digital problems (For metric results, see 11K16)
11A67	其它表示		Other representations
11A99	其它		None of the above, but in this section
11Bxx	序列与集合		Sequences and sets
11B05	稠密性, 间隙, 拓扑		Density, gaps, topology
11B13	加性基, 包括和集[参见05B10]		Additive bases, including sumsets [See also 05B10]
11B25	算术级数[参见11N13]		Arithmetic progressions [See also 11N13]
11B30	算术组合学; 高度一致性		Arithmetic combinatorics; higher degree uniformity
11B34	表示函数		Representation functions
11B37	递归(特殊函数的应用, 见33-XX)		Recurrences (For applications to special functions, see 33-XX)
11B39	Fibonacci数, Lucas数, 多项式及推广		Fibonacci and Lucas numbers and polynomials and generalizations
11B50	序列(模m)		Sequences (mod m)
11B57	Farey序列; 序列1^k, 2^k, …		Farey sequences; the sequences 1^k, 2^k, …
11B65	二项式系数; 阶乘; q-恒等式[参见05A10, 05A30]		Binomial coefficients; factorials; q-identities [See also 05A10, 05A30]
11B68	Bernoulli数, Euler数和多项式		Bernoulli and Euler numbers and polynomials
11B73	Bell数和Stirling数		Bell and Stirling numbers
11B75	其它组合数论		Other combinatorial number theory
11B83	特殊序列和多项式		Special sequences and polynomials
11B85	自动机序列		Automata sequences
11B99	其它		None of the above, but in this section
11Cxx	多项式和矩阵		Polynomials and matrices
11C08	多项式[参见13F20]		Polynomials [See also 13F20]
11C20	矩阵, 行列式[参见15B36]		Matrices, determinants [See also 15B36]
11C99	其它		None of the above, but in this section
11Dxx	Diophantus方程[参见11Gxx, 14Gxx]		Diophantine equations [See also 11Gxx, 14Gxx]
11D04	线性方程		Linear equations
11D07	Frobenius问题		The Frobenius problem
11D09	二次方程和双线性方程		Quadratic and bilinear equations
11D25	三次方程和四次方程		Cubic and quartic equations
11D41	高次方程; Fermat方程		Higher degree equations; Fermat’s equation
11D45	Diophantus方程的计数解		Counting solutions of Diophantine equations
11D57	乘法方程和范数形式方程		Multiplicative and norm form equations
11D59	Thue-Mahler方程		Thue-Mahler equations
11D61	指数方程		Exponential equations
11D68	可作为分数和的有理数		Rational numbers as sums of fractions
11D72	多变量方程[参见11P55]		Equations in many variables [See also 11P55]
11D75	Diophantus不等式[参见11J25]		Diophantine inequalities [See also 11J25]
11D79	多变量同余		Congruences in many variables
11D85	表示问题[参见11P55]		Representation problems [See also 11P55]
11D88	p-进域和幂级数域		p-adic and power series fields
11D99	其它		None of the above, but in this section
11Exx	型和线性代数群[参见19Gxx](线性代数二次型, 见15A63)		Forms and linear algebraic groups [See also 19Gxx] (For quadratic forms in linear algebra, see 15A63)
11E04	一般域上的二次型		Quadratic forms over general fields
11E08	局部环和局部域上的二次型		Quadratic forms over local rings and fields
11E10	实域上的型		Forms over real fields
11E12	整体环和整体域上的二次型		Quadratic forms over global rings and fields
11E16	一般双元二次型		General binary quadratic forms
11E20	一般三元和四元二次型; 多于两个变量的型		General ternary and quaternary quadratic forms; forms of more than two variables
11E25	平方和及其它特殊二次型的表示		Sums of squares and representations by other particular quadratic forms
11E39	双线性型和Hermite型		Bilinear and Hermitian forms
11E41	二次型和Hermite型的类数		Class numbers of quadratic and Hermitian forms
11E45	解析理论(Epstein ζ函数; 与自同构型和函数的关系)		Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
11E57	典型群[参见14Lxx, 20Gxx]		Classical groups [See also 14Lxx, 20Gxx]
11E70	二次型与Hermite型的K-理论		K-theory of quadratic and Hermitian forms
11E72	线性代数群的Galois上同调[参见20G10]		Galois cohomology of linear algebraic groups [See also 20G10]
11E76	高于二次的型		Forms of degree higher than two
11E81	二次型的代数理论; Witt群和环[参见19G12, 19G24]		Algebraic theory of quadratic forms; Witt groups and rings [See also 19G12, 19G24]
11E88	二次空间; Clifford代数[参见15A63, 15A66]		Quadratic spaces; Clifford algebras [See also 15A63, 15A66]
11E95	p-进理论		p-adic theory
11E99	其它		None of the above, but in this section
11Fxx	不连续群和自守形式[参见11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx](与二次型的关系, 见11E45)		Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] (For relations with quadratic forms, see 11E45)
11F03	模函数和自守函数		Modular and automorphic functions
11F06	模群的结构和推广; 算术群[参见20H05, 20H10, 22E40]		Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40]
11F11	积分权重的全纯模形式		Holomorphic modular forms of integral weight
11F12	自守形式, 单变量		Automorphic forms, one variable
11F20	Dedekind η函数, Dedekind和		Dedekind eta function, Dedekind sums
11F22	与Lie代数和有限单群的关系		Relationship to Lie algebras and finite simple groups
11F23	与代数几何和拓扑的关系		Relations with algebraic geometry and topology
11F25	Hecke-Petersson算子, 微分算子(单变量)		Hecke-Petersson operators, differential operators (one variable)
11F27	θ级数; Weil表示;θ对应		Theta series; Weil representation; theta correspondences
11F30	自守形式的Fourier系数		Fourier coefficients of automorphic forms
11F32	模对应等		Modular correspondences, etc.
11F33	模和p-进模形式的同余[参见14G20, 22E50]		Congruences for modular and p-adic modular forms [See also 14G20, 22E50]
11F37	半整数加权形式; 非全纯模形式		Forms of half-integer weight; nonholomorphic modular forms
11F41	GL(2)上的自守形式; Hilbert和Hilbert-Siegel模群及其模形式和自守形式; Hilbert模曲面[参见14J20]		Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
11F46	Siegel模群; Siegel及Hilbert-Siegel模形式和自守形式		Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
11F50	Jacobi形式		Jacobi forms
11F52	与Drinfel'd模有关的模形式		Modular forms associated to Drinfel'd modules
11F55	其它群及其模形式和自守形式(多变量)		Other groups and their modular and automorphic forms (several variables)
11F60	Hecke-Petersson算子, 微分算子(多变量)		Hecke-Petersson operators, differential operators (several variables)
11F66	Langlands L-函数;单变量Dirichlet级数和泛函方程		Langlands L-functions; one variable Dirichlet series and functional equations
11F67	自守L-级数的特殊值, 模形式的周期, 上同调, 模符号		Special values of automorphic L-series, periods of modular forms, cohomology, modular symbols
11F68	多复变量中与自守形式相关的Dirichlet级数; Weyl群多重Dirichlet级数		Dirichlet series in several complex variables associated to automorphic forms; Weyl group multiple Dirichlet series
11F70	表示理论的方法; 局部域和整体域上的自守表示		Representation-theoretic methods; automorphic representations over local and global fields
11F72	谱理论; Selberg迹公式		Spectral theory; Selberg trace formula
11F75	算术群的上同调		Cohomology of arithmetic groups
11F80	Galois表示		Galois representations
11F85	p-进理论, 局部域[参见14G20, 22E50]		p-adic theory, local fields [See also 14G20, 22E50]
11F99	其它		None of the above, but in this section
11Gxx	算术代数几何(Diophantus几何)[参见11Dxx, 14Gxx, 14Kxx]		Arithmetic algebraic geometry (Diophantine geometry) [See also 11Dxx, 14Gxx, 14Kxx]
11G05	整体域上的椭圆曲线[参见14H52]		Elliptic curves over global fields [See also 14H52]
11G07	局部域上的椭圆曲线[参见14G20, 14H52]		Elliptic curves over local fields [See also 14G20, 14H52]
11G09	Drinfel'd模; 高维运动等[参见14L05]		Drinfel'd modules; higher-dimensional motives, etc. [See also 14L05]
11G10	维数>1的Abel簇[参见14Kxx]		Abelian varieties of dimension >1 [See also 14Kxx]
11G15	Abel簇的复数乘法和模数[参见14K22]		Complex multiplication and moduli of abelian varieties [See also 14K22]
11G16	椭圆单位和模单位[参见11R27]		Elliptic and modular units [See also 11R27]
11G18	模和Shimura簇的算术方面[参见14G35]		Arithmetic aspects of modular and Shimura varieties [See also 14G35]
11G20	有限域和局部域上的曲线[参见14H25]		Curves over finite and local fields [See also 14H25]
11G25	有限域和局部域上的簇[参见14G15, 14G20]		Varieties over finite and local fields [See also 14G15, 14G20]
11G30	整体域上任意亏格或亏格≠1的曲线[参见14H25]		Curves of arbitrary genus or genus ≠1 over global fields [See also 14H25]
11G32	Dessins d'enfants, Belyǐ理论		Dessins d'enfants, Belyǐ theory
11G35	整体域上的簇[参见14G25]		Varieties over global fields [See also 14G25]
11G40	整体域上簇的L-函数; Birch-Swinnerton-Dyer猜想[参见14G10]		L-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
11G42	算术镜对称[参见14J33]		Arithmetic mirror symmetry [See also 14J33]
11G45	几何类域理论[参见11R37, 14C35, 19F05]		Geometric class field theory [See also 11R37, 14C35, 19F05]
11G50	高度[参见14G40, 37P30]		Heights [See also 14G40, 37P30]
11G55	多对数及与K-理论的关系		Polylogarithms and relations with K-theory
11G99	其它		None of the above, but in this section
11Hxx	数的几何(在编码理论中的应用, 见94B75)		Geometry of numbers (For applications in coding theory, see 94B75)
11H06	格与凸体[参见11P21, 52C05, 52C07]		Lattices and convex bodies [See also 11P21, 52C05, 52C07]
11H16	非凸体		Nonconvex bodies
11H31	格填装与覆盖[参见05B40, 52C15, 52C17]		Lattice packing and covering [See also 05B40, 52C15, 52C17]
11H46	线性型的积		Products of linear forms
11H50	型的极小值		Minima of forms
11H55	二次型(约化理论、极型等)		Quadratic forms (reduction theory, extreme forms, etc.)
11H56	格的自同构群		Automorphism groups of lattices
11H60	均值与转移定理		Mean value and transfer theorems
11H71	与编码理论的关系		Relations with coding theory
11H99	其它		None of the above, but in this section
11Jxx	Diophantus逼近, 超越数理论[参见11K60]		Diophantine approximation, transcendental number theory [See also 11K60]
11J04	一个数的齐次逼近		Homogeneous approximation to one number
11J06	Markov谱和Lagrange谱及推广		Markov and Lagrange spectra and generalizations
11J13	联立齐次逼近, 线性型		Simultaneous homogeneous approximation, linear forms
11J17	固定域中数逼近		Approximation by numbers from a fixed field
11J20	非齐次线性型		Inhomogeneous linear forms
11J25	Diophantus不等式[参见11D75]		Diophantine inequalities [See also 11D75]
11J54	多项式小分式部分及推广		Small fractional parts of polynomials and generalizations
11J61	非Archimedes赋值中的逼近		Approximation in non-Archimedean valuations
11J68	代数数逼近		Approximation to algebraic numbers
11J70	连分数及推广[参见11A55, 11K50]		Continued fractions and generalizations [See also 11A55, 11K50]
11J71	分布模1[参见11K06]		Distribution modulo one [See also 11K06]
11J72	无理性; 域上的线性独立性		Irrationality; linear independence over a field
11J81	超越性(一般理论)		Transcendence (general theory)
11J82	无理性和超越性的测度		Measures of irrationality and of transcendence
11J83	度量理论		Metric theory
11J85	代数独立性; Gel'fond方法		Algebraic independence; Gel'fond’s method
11J86	对数中的线性型; Baker方法		Linear forms in logarithms; Baker’s method
11J87	Schmidt子空间定理及应用		Schmidt subspace theorem and applications
11J89	椭圆函数和Abel函数的超越理论		Transcendence theory of elliptic and abelian functions
11J91	其它特殊函数的超越理论		Transcendence theory of other special functions
11J93	Drinfel'd和t-模的超越理论		Transcendence theory of Drinfel'd and t-modules
11J95	涉及Abel簇的结果		Results involving abelian varieties
11J97	Nevanlinna理论中方法的模拟(Vojta等的工作)		Analogues of methods in Nevanlinna theory (work of Vojta et al.)
11J99	其它		None of the above, but in this section
11Kxx	概率理论: 分布模1; 算法度量理论		Probabilistic theory: distribution modulo 1; metric theory of algorithms
11K06	分布模1的一般理论[参见11J71]		General theory of distribution modulo 1 [See also 11J71]
11K16	正规数, 基数展开, Pisot数, Salem数, 好格点等[参见11A63]		Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
11K31	特殊序列		Special sequences
11K36	Well分布序列和其它变差		Well-distributed sequences and other variations
11K38	分布的不规则性, 不一致性[参见11Nxx]		Irregularities of distribution, discrepancy [See also 11Nxx]
11K41	连续, p-进和抽象模拟		Continuous, p-adic and abstract analogues
11K45	伪随机数; Monte Carlo方法		Pseudo-random numbers; Monte Carlo methods
11K50	连分数度量理论[参见11A55, 11J70]		Metric theory of continued fractions [See also 11A55, 11J70]
11K55	其它算法的度量理论和展开; 测度与Hausdorff维数[参见11N99, 28Dxx]		Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
11K60	Diophantus逼近[参见11Jxx]		Diophantine approximation [See also 11Jxx]
11K65	算术函数[参见11Nxx]		Arithmetic functions [See also 11Nxx]
11K70	调和分析与殆周期性		Harmonic analysis and almost periodicity
11K99	其它		None of the above, but in this section
11Lxx	指数和与特征和(有限域, 见11Txx)		Exponential sums and character sums (For finite fields, see 11Txx)
11L03	三角和与指数和, 一般问题		Trigonometric and exponential sums, general
11L05	Gauss和与Kloosterman和; 推广		Gauss and Kloosterman sums; generalizations
11L07	指数和估计		Estimates on exponential sums
11L10	Jacobsthal和与Brewer和; 其它完备特征和		Jacobsthal and Brewer sums; other complete character sums
11L15	Wey1和		Weyl sums
11L20	素数上的和		Sums over primes
11L26	任意区间上的和		Sums over arbitrary intervals
11L40	特征和的估计		Estimates on character sums
11L99	其它		None of the above, but in this section
11Mxx	ζ函数与L-函数: 解析理论		Zeta and L-functions: analytic theory
11M06	ζ(s)和L(s, χ)		ζ(s) and L(s, χ)
11M20	L(s, χ)的实零点; 关于L(1, χ)的结果		Real zeros of L(s, χ); results on L(1, χ)
11M26	ζ(s)和L(s, χ)的非实零点; Riemann和其它假设		Nonreal zeros ofζ(s) and L(s, χ); Riemann and other hypotheses
11M32	多重 Dirichlet级数和ζ函数以及多ζ值		Multiple Dirichlet series and zeta functions and multizeta values
11M35	Hurwitz和Lerch ζ函数		Hurwitz and Lerch zeta functions
11M36	Selberg ζ函数和正则化行列式; 应用于谱论、Dirichlet级数、Eisenstein级数等显式公式		Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. explicit formulas
11M38	特征p中的ζ函数和L-函数		Zeta and L-functions in characteristic p
11M41	其它Dirichlet级数与ζ函数(局部和整体基本域, 见11R42, 11R52, 11S40, 11S45; 代数几何方法, 见14G10; 参见11E45, 11F66, 11F70, 11F72)		Other Dirichlet series and zeta functions (For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72)
11M45	Tauber定理[参见40E05]		Tauberian theorems [See also 40E05]
11M50	与随机矩阵的关系		Relations with random matrices
11M55	与非交换几何的关系		Relations with noncommutative geometry
11M99	其它		None of the above, but in this section
11Nxx	乘法数论		Multiplicative number theory
11N05	素数分布		Distribution of primes
11N13	级数中的素数[参见11B25]		Primes in progressions [See also 11B25]
11N25	带特殊乘法约束的整数分布		Distribution of integers with specified multiplicative constraints
11N30	Turán理论[参见30Bxx]		Turán theory [See also 30Bxx]
11N32	用多项式表示的素数; 多项式值的其它乘法结构		Primes represented by polynomials; other multiplicative structure of polynomial values
11N35	筛法		Sieves
11N36	筛法的应用		Applications of sieve methods
11N37	算术函数的渐近结果		Asymptotic results on arithmetic functions
11N45	代数与拓扑结构的计数函数的渐近结果		Asymptotic results on counting functions for algebraic and topological structures
11N56	算术函数的增长率		Rate of growth of arithmetic functions
11N60	与加法和正乘法函数相关的分布函数		Distribution functions associated with additive and positive multiplicative functions
11N64	算术函数的值分布或特征的其它结果		Other results on the distribution of values or the characterization of arithmetic functions
11N69	特殊剩余类中的整数分布		Distribution of integers in special residue classes
11N75	自守函数与型在乘法问题中的应用[参见11Fxx]		Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]
11N80	广义素数与整数		Generalized primes and integers
11N99	其它		None of the above, but in this section
11Pxx	堆垒数论; 划分		Additive number theory; partitions
11P05	Waring问题及变量		Waring’s problem and variants
11P21	特殊区域中的格点		Lattice points in specified regions
11P32	Goldbach型定理; 包含素数的其它堆垒问题		Goldbach-type theorems; other additive questions involving primes
11P55	Hardy-Littlewood方法的应用[参见11D85]		Applications of the Hardy-Littlewood method [See also 11D85]
11P70	堆垒数论的逆问题, 包括和集		Inverse problems of additive number theory, including sumsets
11P81	划分的基本理论[参见05A17]		Elementary theory of partitions [See also 05A17]
11P82	划分的解析理论		Analytic theory of partitions
11P83	划分; 同余和同余限制		Partitions; congruences and congruential restrictions
11P84	划分恒等式; Rogers-Ramanujan型恒等式		Partition identities; identities of Rogers-Ramanujan type
11P99	其它		None of the above, but in this section
11Rxx	代数数论: 整体域(复数乘法, 见11G15)		Algebraic number theory: global fields (For complex multiplication, see 11G15)
11R04	代数数; 代数整数环		Algebraic numbers; rings of algebraic integers
11R06	PV数及其推广; 其它特殊的代数数; Mahler测度		PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11R09	多项式(不可约性等)		Polynomials (irreducibility, etc.)
11R11	二次扩张		Quadratic extensions
11R16	三次和四次扩张		Cubic and quartic extensions
11R18	割圆扩张		Cyclotomic extensions
11R20	其它Abel扩张与亚Abel扩张		Other abelian and metabelian extensions
11R21	其它数域		Other number fields
11R23	Iwasawa理论		Iwasawa theory
11R27	单位与因式分解		Units and factorization
11R29	类数, 类群, 判别式		Class numbers, class groups, discriminants
11R32	Galois理论		Galois theory
11R33	关于代数数的整数表示; 整数环的Galois模结构[参见20C10]		Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
11R34	Galois上同调[参见12Gxx, 19A31]		Galois cohomology [See also 12Gxx, 19A31]
11R37	类域理论		Class field theory
11R39	Langlands-Weil猜想, 非Abel类域理论[参见11Fxx, 22E55]		Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
11R42	数域的ζ函数和L-函数[参见11M41, 19F27]		Zeta functions and L-functions of number fields [See also 11M41, 19F27]
11R44	素理论分布[参见11N05]		Distribution of prime ideals [See also 11N05]
11R45	密度定理		Density theorems
11R47	其它解析理论[参见11Nxx]		Other analytic theory [See also 11Nxx]
11R52	四元数与其它可除代数: 算术, ζ函数		Quaternion and other division algebras: arithmetic, zeta functions
11R54	其它代数与整环, 及其ζ函数与L-函数[参见11S45, 16H05, 16Kxx]		Other algebras and orders, and their zeta and L-functions [See also 11S45, 16H05, 16Kxx]
11R56	Adèle环与群		Adèle rings and groups
11R58	代数函数域的算术理论[参见14-XX]		Arithmetic theory of algebraic function fields [See also 14-XX]
11R60	割圆函数域(类群、Bernoulli目标等)		Cyclotomic function fields (class groups, Bernoulli objects, etc.)
11R65	整环的类群和Picard群		Class groups and Picard groups of orders
11R70	整体域的K-理论[参见19Fxx]		K-theory of global fields [See also 19Fxx]
11R80	全实域[参见12J15]		Totally real fields [See also 12J15]
11R99	其它		None of the above, but in this section
11Sxx	代数数论: 局部域和p-进域		Algebraic number theory: local and p-adic fields
11S05	多项式		Polynomials
11S15	分歧与扩张理论		Ramification and extension theory
11S20	Galois理论		Galois theory
11S23	整数表示		Integral representations
11S25	Galois上同调[参见12Gxx, 16H05]		Galois cohomology [See also 12Gxx, 16H05]
11S31	类域理论; p-进形式群[参见14L05]		Class field theory; p-adic formal groups [See also 14L05]
11S37	Langlands-Weil猜想, 非Abel类域理论[参见11Fxx, 22E50]		Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
11S40	ζ函数与L-函数[参见11M41, 19F27]		Zeta functions and L-functions [See also 11M41, 19F27]
11S45	代数和整环, 及其ζ函数[参见11R52, 11R54, 16Hxx, 16Kxx]		Algebras and orders, and their zeta functions [See also 11R52, 11R54, 16Hxx, 16Kxx]
11S70	局部域的K-理论[参见19Fxx]		K-theory of local fields [See also 19Fxx]
11S80	其它解析理论(β函数和Γ函数的模拟、p-进积分法等)		Other analytic theory (analogues of beta and gamma functions, p-adic integration, etc.)
11S82	非Archimedes动力系统[主要见 37Pxx]		Non-Archimedean dynamical systems [See mainly 37Pxx]
11S85	其它非解析理论		Other nonanalytic theory
11S90	准齐性向量空间		Prehomogeneous vector spaces
11S99	其它		None of the above, but in this section
11Txx	有限域和有限交换环(数论方面)		Finite fields and commutative rings (number-theoretic aspects)
11T06	多项式		Polynomials
11T22	割圆		Cyclotomy
11T23	指数和		Exponential sums
11T24	其它特征和与高斯和		Other character sums and Gauss sums
11T30	结构理论		Structure theory
11T55	有限域上多项式环的算术理论		Arithmetic theory of polynomial rings over finite fields
11T60	有限上半平面		Finite upper half-planes
11T71	代数编码理论; 密码学		Algebraic coding theory; cryptography
11T99	其它		None of the above, but in this section
11Uxx	与逻辑的联系		Connections with logic
11U05	可判定性[参见03B25]		Decidability [See also 03B25]
11U07	超积[参见03C20]		Ultraproducts [See also 03C20]
11U09	模型论[参见03Cxx]		Model theory [See also 03Cxx]
11U10	非标准算术[参见03H15]		Nonstandard arithmetic [See also 03H15]
11U99	其它		None of the above, but in this section
11Yxx	计算数论[参见11-04]		Computational number theory [See also 11-04]
11Y05	因子分解		Factorization
11Y11	基本性质		Primality
11Y16	算法; 复杂性[参见68Q25]		Algorithms; complexity [See also 68Q25]
11Y35	解析计算		Analytic computations
11Y40	代数数论计算		Algebraic number theory computations
11Y50	Diophantus方程的计算机解		Computer solution of Diophantine equations
11Y55	整数序列的计算		Calculation of integer sequences
11Y60	常数的赋值		Evaluation of constants
11Y65	连分式计算		Continued fraction calculations
11Y70	算术函数值; 表格		Values of arithmetic functions; tables
11Y99	其它		None of the above, but in this section
11Zxx	数论的其它应用		Miscellaneous applications of number theory
11Z05	数论的其它应用		Miscellaneous applications of number theory
11Z99	其它		None of the above, but in this section
12-XX	域论和多项式		Field theory and polynomials
12-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
12-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
12-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
12-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
12-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
12-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
12Dxx	实域和复域		Real and complex fields
12D05	多项式: 因式分解		Polynomials: factorization
12D10	多项式: 零点的位置(代数定理)(解析理论, 见26C10, 30C15)		Polynomials: location of zeros (algebraic theorems) (For the analytic theory, see 26C10, 30C15)
12D15	与平方和有关的域(形式实域、Pythagoras域等)[参见11Exx]		Fields related with sums of squares (formally real fields, Pythagorean fields, etc.) [See also 11Exx]
12D99	其它		None of the above, but in this section
12Exx	一般域论		General field theory
12E05	多项式(不可约性等)		Polynomials (irreducibility, etc.)
12E10	特殊多项式		Special polynomials
12E12	方程		Equations
12E15	斜域, 除环[参见11R52, 11R54, 11S45, 16Kxx]		Skew fields, division rings [See also 11R52, 11R54, 11S45, 16Kxx]
12E20	有限域(域论方面)		Finite fields (field-theoretic aspects)
12E25	Hilbert域; Hilbert不可约性定理		Hilbertian fields; Hilbert’s irreducibility theorem
12E30	域算术		Field arithmetic
12E99	其它		None of the above, but in this section
12Fxx	域扩张		Field extensions
12F05	代数扩张		Algebraic extensions
12F10	可分扩张, Galois理论		Separable extensions, Galois theory
12F12	逆Galois理论		Inverse Galois theory
12F15	不可分扩张		Inseparable extensions
12F20	超越扩张		Transcendental extensions
12F99	其它		None of the above, but in this section
12Gxx	同调方法(域论)		Homological methods (field theory)
12G05	Galois上同调[参见14F22, 16Hxx, 16K50]		Galois cohomology [See also 14F22, 16Hxx, 16K50]
12G10	上同调维数		Cohomological dimension
12G99	其它		None of the above, but in this section
12Hxx	微分代数与差分代数		Differential and difference algebra
12H05	微分代数[参见13Nxx]		Differential algebra [See also 13Nxx]
12H10	差分代数[参见39Axx]		Difference algebra [See also 39Axx]
12H20	抽象微分方程[参见34Mxx]		Abstract differential equations [See also 34Mxx]
12H25	p-进微分方程[参见11S80, 14G20]		p-adic differential equations [See also 11S80, 14G20]
12H99	其它		None of the above, but in this section
12Jxx	拓扑域		Topological fields
12J05	赋范域		Normed fields
12J10	值域		Valued fields
12J12	形式p-进域		Formally p-adic fields
12J15	有序域		Ordered fields
12J17	扑拓半域		Topological semifields
12J20	一般赋值理论[参见13A18]		General valuation theory [See also 13A18]
12J25	非Archimedes值域[参见30G06, 32P05, 46S10, 47S10]		Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10]
12J27	Krasner-Tate代数[主要见32P05; 参见46S10, 47S10]		Krasner-Tate algebras [See mainly 32P05; see also 46S10, 47S10]
12J99	其它		None of the above, but in this section
12Kxx	域的推广		Generalizations of fields
12K05	拟域[参见16Y30]		Near-fields [See also 16Y30]
12K10	半域[参见16Y60]		Semifields [See also 16Y60]
12K99	其它		None of the above, but in this section
12Lxx	与逻辑的联系		Connections with logic
12L05	可判定性[参见03B25]		Decidability [See also 03B25]
12L10	超积[参见03C20]		Ultraproducts [See also 03C20]
12L12	模型论[参见03C60]		Model theory [See also 03C60]
12L15	非标准算术[参见03H15]		Nonstandard arithmetic [See also 03H15]
12L99	其它		None of the above, but in this section
12Yxx	域论和多项式的计算方面		Computational aspects of field theory and polynomials
12Y05	域论和多项式的计算方面		Computational aspects of field theory and polynomials
12Y99	其它		None of the above, but in this section
13-XX	交换代数		Commutative algebras
13-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
13-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
13-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
13-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
13-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
13-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
13Axx	一般交换环理论		General commutative ring theory
13A02	分次环[参见16W50]		Graded rings [See also 16W50]
13A05	整除性; 因式分解[参见13F15]		Divisibility; factorizations [See also 13F15]
13A15	理想; 乘法理想理论		Ideals; multiplicative ideal theory
13A18	赋值及其推广[参见12J20]		Valuations and their generalizations [See also 12J20]
13A30	理想的结合分次环(Rees环, 形式环), 解析扩展和有关论题		Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13A35	特征p方法(Frobenius自同态)与特征p约化; 胎紧闭包[参见13B22]		Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
13A50	交换环上群的作用; 不变量理论[参见14L24]		Actions of groups on commutative rings; invariant theory [See also 14L24]
13A99	其它		None of the above, but in this section
13Bxx	环扩张及相关课题		Ring extensions and related topics
13B02	扩张理论		Extension theory
13B05	Galois理论		Galois theory
13B10	态射		Morphisms
13B21	整相关; 上升, 下降		Integral dependence; going up, going down
13B22	环和理想的整闭包[参见13A35]; 整闭环, 相关环(日本的等)		Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.)
13B25	交换环上的多项式[参见11C08, 11T06, 13F20, 13M10]		Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10]
13B30	分式环与局部化[参见16S85]		Rings of fractions and localization [See also 16S85]
13B35	完备化[参见13J10]		Completion [See also 13J10]
13B40	Étale和平坦扩张; Hensel化; Artin逼近[参见13J15, 14B12, 14B25]		Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
13B99	其它		None of the above, but in this section
13Cxx	模和理想理论		Theory of modules and ideals
13C05	结构, 分类定理		Structure, classification theorems
13C10	射影与自由模以及理想[参见19A13]		Projective and free modules and ideals [See also 19A13]
13C11	内射与平坦模以及理想		Injective and flat modules and ideals
13C12	挠模与理想		Torsion modules and ideals
13C13	其它特殊类型		Other special types
13C14	Cohen-Macaulay模[参见13H10]		Cohen-Macaulay modules [See also 13H10]
13C15	维数理论, 深度, 相关环(悬链线等)		Dimension theory, depth, related rings (catenary, etc.)
13C20	类群[参见11R29]		Class groups [See also 11R29]
13C40	环绕, 完全相交与行列式理想[参见14M06, 14M10, 14M12]		Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12]
13C60	模范畴		Module categories
13C99	其它		None of the above, but in this section
13Dxx	(上)同调方法(非交换环, 见16Exx; 一般范畴, 见18Gxx)		Homological methods (For noncommutative rings, see 16Exx; for general categories, see 18Gxx)
13D02	合冲与预解, 复合		Syzygies and resolutions, complexes
13D03	交换环与交换代数的(上)同调(例如: Hochschild、André-Quillen、循环、二面体等)		(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
13D05	(上)同调维数		Homological dimension
13D07	模上的同调函子(Tor、Ext等)		Homological functors on modules (Tor, Ext, etc.)
13D09	导出范畴		Derived categories
13D10	变形和无穷小方法[参见14B10, 14B12, 14D15, 32Gxx]		Deformations and infinitesimal methods [See also 14B10, 14B12, 14D15, 32Gxx]
13D15	Grothendieck群, K-理论[参见14C35, 18F30, 19Axx, 19D50]		Grothendieck groups, K-theory [See also 14C35, 18F30, 19Axx, 19D50]
13D22	同调猜想(相交定理)		Homological conjectures (intersection theorems)
13D30	挠理论[参见13C12, 18E40]		Torsion theory [See also 13C12, 18E40]
13D40	Hilbert-Samuel函数和Hilbert-Kunz函数; Poincaré级数		Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
13D45	局部上同调[参见14B15]		Local cohomology [See also 14B15]
13D99	其它		None of the above, but in this section
13Exx	链条件, 有限性条件		Chain conditions, finiteness conditions
13E05	Noether环与模		Noetherian rings and modules
13E10	Artin环与模, 有限维代数		Artinian rings and modules, finite-dimensional algebras
13E15	有限生成或表示的环与模; 生成元的数		Rings and modules of finite generation or presentation; number of generators
13E99	其它		None of the above, but in this section
13Fxx	算术环与其它特殊环		Arithmetic rings and other special rings
13F05	Dedekind环, Prüfer环, Krull环和Mori环及其推广		Dedekind, Prüfer, Krull and Mori rings and their generalizations
13F07	Euclid环及其推广		Euclidean rings and generalizations
13F10	主理想环		Principal ideal rings
13F15	由因式分解性质定义的环(例如: 原子, 阶乘, 半阶乘)[参见13A05, 14M05]		Rings defined by factorization properties (e.g., atomic, factorial, half-factorial) [See also 13A05, 14M05]
13F20	多项式环和理想; 整数值多项式的环[参见11C08, 13B25]		Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25]
13F25	形式幂级数环[参见13J05]		Formal power series rings [See also 13J05]
13F30	赋值环[参见13A18]		Valuation rings [See also 13A18]
13F35	Witt向量及相关环		Witt vectors and related rings
13F40	优环		Excellent rings
13F45	半正规环		Seminormal rings
13F50	直化律环, Hodge代数		Rings with straightening laws, Hodge algebras
13F55	Stanley-Reisner面环; 单纯复形[参见55U10]		Stanley-Reisner face rings; simplicial complexes [See also 55U10]
13F60	聚类代数		Cluster algebras
13F99	其它		None of the above, but in this section
13Gxx	整体域		Integral domains
13G05	整体域		Integral domains
13G99	其它		None of the above, but in this section
13Hxx	局部环和半局部环		Local rings and semilocal rings
13H05	正则局部环		Regular local rings
13H10	特殊类型(Cohen-Macaulay、Gorenstein、Buchsbaum等)[参见14M05]		Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
13H15	乘法理论与相关课题[参见14C17]		Multiplicity theory and related topics [See also 14C17]
13H99	其它		None of the above, but in this section
13Jxx	拓扑环和模[参见16W60, 16W80]		Topological rings and modules [See also 16W60, 16W80]
13J05	幂级数环[参见13F25]		Power series rings [See also 13F25]
13J07	解析代数和解析环[参见32B05]		Analytical algebras and rings [See also 32B05]
13J10	完备环, 完备化[参见13B35]		Complete rings, completion [See also 13B35]
13J15	Hensel环[参见13B40]		Henselian rings [See also 13B40]
13J20	整体拓扑环		Global topological rings
13J25	有序环[参见06F25]		Ordered rings [See also 06F25]
13J30	实代数[参见12D15, 14Pxx]		Real algebra [See also 12D15, 14Pxx]
13J99	其它		None of the above, but in this section
13Lxx	逻辑应用于交换代数[参见03Cxx, 03Hxx]		Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
13L05	逻辑应用于交换代数[参见03Cxx, 03Hxx]		Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
13L99	其它		None of the above, but in this section
13Mxx	有限交换环(数论方面, 见11Txx)		Finite commutative rings (For number-theoretic aspects, see 11Txx)
13M05	结构		Structure
13M10	多项式		Polynomials
13M99	其它		None of the above, but in this section
13Nxx	微分代数[参见12H05, 14F10]		Differential algebra [See also 12H05, 14F10]
13N05	微分模		Modules of differentials
13N10	微分算子环及其模[参见16S32, 32C38]		Rings of differential operators and their modules [See also 16S32, 32C38]
13N15	求导		Derivations
13N99	其它		None of the above, but in this section
13Pxx	计算方面和应用[参见14Qxx, 68W30]		Computational aspects and applications [See also 14Qxx, 68W30]
13P05	多项式, 因式分解[参见12Y05]		Polynomials, factorization [See also 12Y05]
13P10	Gröbner基; 理想和模的其它基(例如: Janet基和边界基)		Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13P15	解多项式系统; 结式		Solving polynomial systems; resultants
13P20	计算同调代数[参见13Dxx]		Computational homological algebra [See also 13Dxx]
13P25	交换代数的应用(例如: 统计学、控制理论、最优化等)		Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
13P99	其它		None of the above, but in this section
14-XX	代数几何		Algebraic geometry
14-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
14-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
14-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
14-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
14-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
14-05	会议录、会议、文集等		Proceedings, conferences, collections, etc.
14Axx	基础		Foundations
14A05	相关交换代数[参见13-XX]		Relevant commutative algebra [See also 13-XX]
14A10	簇和态射		Varieties and morphisms
14A15	概型和态射		Schemes and morphisms
14A20	推广(代数空间, 叠加)		Generalizations (algebraic spaces, stacks)
14A22	非交换代数几何[参见16S38]		Noncommutative algebraic geometry [See also 16S38]
14A25	基本问题		Elementary questions
14A99	其它		None of the above, but in this section
14Bxx	局部理论		Local theory
14B05	奇异性[参见14E15, 14H20, 14J17, 32Sxx, 58Kxx]		Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]
14B07	奇异性的形变[参见14D15, 32S30]		Deformations of singularities [See also 14D15, 32S30]
14B10	无穷小方法[参见13D10]		Infinitesimal methods [See also 13D10]
14B12	局部形变理论、Artin逼近等[参见13B40, 13D10]		Local deformation theory, Artin approximation, etc. [See also 13B40, 13D10]
14B15	局部上同调[参见13D45, 32C36]		Local cohomology [See also 13D45, 32C36]
14B20	形式邻域		Formal neighborhoods
14B25	态射的局部结构: étale、平坦等[参见13B40]		Local structure of morphisms: étale, flat, etc. [See also 13B40]
14B99	其它		None of the above, but in this section
14Cxx	循环与子概型		Cycles and subschemes
14C05	参数化(Chow和Hilbert概型)		Parametrization (Chow and Hilbert schemes)
14C15	(等变的)Chow群和环; motives		(Equivariant) Chow groups and rings; motives
14C17	相交理论, 特征类, 相交重数[参见13H15]		Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
14C20	除子, 线性系统, 可逆层		Divisors, linear systems, invertible sheaves
14C21	束, 网, 罗[参见53A60]		Pencils, nets, webs [See also 53A60]
14C22	Picard群		Picard groups
14C25	代数闭链		Algebraic cycles
14C30	超越方法, Hodge理论[参见14D07, 32G20, 32J25, 32S35], Hodge猜想		Transcendental methods, Hodge theory [See also 14D07, 32G20, 32J25, 32S35], Hodge conjecture
14C34	Torelli问题[参见32G20]		Torelli problem [See also 32G20]
14C35	代数K-理论方法的应用[参见19Exx]		Applications of methods of algebraic K-theory [See also 19Exx]
14C40	Riemann-Roch定理[参见19E20, 19L10]		Riemann-Roch theorems [See also 19E20, 19L10]
14C99	其它		None of the above, but in this section
14Dxx	族, 纤维化		Families, fibrations
14D05	族的结构(Picard-Lefschetz理论、单值[性]等)		Structure of families (Picard-Lefschetz, monodromy, etc.)
14D06	纤维化, 退化		Fibrations, degenerations
14D07	Hodge结构的变分[参见32G20]		Variation of Hodge structures [See also 32G20]
14D10	算术基域(有限, 局部, 整体)		Arithmetic ground fields (finite, local, global)
14D15	形式方法; 形变[参见13D10, 14B07, 32Gxx]		Formal methods; deformations [See also 13D10, 14B07, 32Gxx]
14D20	代数模问题, 向量丛的模(解析模问题, 见32G13)		Algebraic moduli problems, moduli of vector bundles (For analytic moduli problems, see 32G13)
14D21	数学物理中向量丛和模空间的应用(扭子理论, 瞬子, 量子场论)		Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14D22	细与粗模空间		Fine and coarse moduli spaces
14D23	叠加和模问题		Stacks and moduli problems
14D24	几何Langlands程序: 代数几何方面[参见22E57]		Geometric Langlands program: algebrogeometric aspects [See also 22E57]
14D99	其它		None of the above, but in this section
14Exx	双有理几何		Birational geometry
14E05	有理映射和双有理映射		Rational and birational maps
14E07	双有理自同构, Cremona群及推广		Birational automorphisms, Cremona group and generalizations
14E08	有理性问题[参见14M20]		Rationality questions [See also 14M20]
14E15	整体理论和奇异性分解[参见14B05, 32S20, 32S45]		Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]
14E16	McKay对应		McKay correspondence
14E18	弧与主积分法		Arcs and motivic integration
14E20	覆盖[参见14H30]		Coverings [See also 14H30]
14E22	分歧问题[参见11S15]		Ramification problems [See also 11S15]
14E25	嵌入		Embeddings
14E30	极小模型程序(Mori理论, 极值射线)		Minimal model program (Mori theory, extremal rays)
14E99	其它		None of the above, but in this section
14Fxx	(上)同调理论[参见13Dxx]		(Co)homology theory [See also 13Dxx]
14F05	层, 层的导出范畴及相关构造[参见14H60, 14J60, 18F20, 32Lxx, 46M20]		Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
14F10	微分层和其它特殊层; D-modules; Bernstein-Sato理想及多项式[参见13Nxx, 32C38]		Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38]
14F17	消没定理[参见32L20]		Vanishing theorems [See also 32L20]
14F18	乘法理想		Multiplier ideals
14F20	Étale与其它Grothendieck拓扑和上同调		Étale and other Grothendieck topologies and cohomologies
14F22	概形的Brauer群[参见12G05, 16K50]		Brauer groups of schemes [See also 12G05, 16K50]
14F25	经典实上同调和复上同调		Classical real and complex cohomology
14F30	p-进上同调, 结晶线上同调		p-adic cohomology, crystalline cohomology
14F35	同调论; 基本群[参见14H30]		Homotopy theory; fundamental groups [See also 14H30]
14F40	de Rham上同调[参见14C30, 32C35, 32L10]		de Rham cohomology [See also 14C30, 32C35, 32L10]
14F42	主上同调; 主同伦理论		Motivic cohomology; motivic homotopy theory
14F43	其它代数-几何(上)同调(例如: 相交、等变、Lawson、Deligne(上)同调)		Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
14F45	拓扑性质		Topological properties
14F99	其它		None of the above, but in this section
14Gxx	算术问题, Diophantus几何[参见11Dxx, 11Gxx]		Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx]
14G05	有理点		Rational points
14G10	ζ函数与相关问题[参见11G40](Birch-Swinnerton-Dyer猜想)		Zeta-functions and related questions [See also 11G40] (Birch-Swinnerton-Dyer conjecture)
14G15	有限基域		Finite ground fields
14G17	正特征基域		Positive characteristic ground fields
14G20	局部基域		Local ground fields
14G22	刚性解析几何		Rigid analytic geometry
14G25	整体基域		Global ground fields
14G27	其它非代数闭基域		Other nonalgebraically closed ground fields
14G32	泛投射有限群(与模空间, 映射和模塔, Galois理论的关系)		Universal profinite groups (relationship to moduli spaces, projective and moduli towers, Galois theory)
14G35	模和Shimura簇[参见11F41, 11F46, 11G18]		Modular and Shimura varieties [See also 11F41, 11F46, 11G18]
14G40	算术簇和概型; Arakelov理论; 高度[参见11G50, 37P30]		Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
14G50	应用于编码理论和密码学[参见94A60, 94B27, 94B40]		Applications to coding theory and cryptography [See also 94A60, 94B27, 94B40]
14G99	其它		None of the above, but in this section
14Hxx	曲线		Curves
14H05	代数函数; 函数域[参见11R58]		Algebraic functions; function fields [See also 11R58]
14H10	族, 模(代数的)		Families, moduli (algebraic)
14H15	族, 模(解析的)[参见30F10, 32Gxx]		Families, moduli (analytic) [See also 30F10, 32Gxx]
14H20	奇异性, 局部环[参见13Hxx, 14B05]		Singularities, local rings [See also 13Hxx, 14B05]
14H25	算术基域[参见11Dxx, 11G05, 14Gxx]		Arithmetic ground fields [See also 11Dxx, 11G05, 14Gxx]
14H30	覆盖, 基本群[参见14E20, 14F35]		Coverings, fundamental group [See also 14E20, 14F35]
14H37	自同构		Automorphisms
14H40	Jacobi行列式, Prym簇[参见32G20]		Jacobians, Prym varieties [See also 32G20]
14H42	θ函数; Schottky问题[参见14K25, 32G20]		Theta functions; Schottky problem [See also 14K25, 32G20]
14H45	特殊曲线和低亏格曲线		Special curves and curves of low genus
14H50	平面和空间曲线		Plane and space curves
14H51	特殊除子(gonality, Brill-Noether理论)		Special divisors (gonality, Brill-Noether theory)
14H52	椭圆曲线[参见11G05, 11G07, 14Kxx]		Ellipse curve [See also 11G05, 11G07, 14Kxx]
14H55	Riemann曲面; Weierstrass点; 间断序列[参见30Fxx]		Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]
14H57	Dessins d'enfants理论(算术方面, 见11G32)		Dessins d'enfants theory (For arithmetic aspects, see 11G32)
14H60	曲线上的向量丛及其模[参见14D20, 14F05]		Vector bundles on curves and their moduli [See also 14D20, 14F05]
14H70	与可积系统的关系		Relationships with integrable systems
14H81	与物理的关系		Relationships with physics
14H99	其它		None of the above, but in this section
14Jxx	曲面与高维簇(解析理论, 见32Jxx)		Surfaces and higher-dimensional varieties (For analytic theory, see 32Jxx)
14J10	族, 模, 分类: 代数理论		Families, moduli, classification: algebraic theory
14J15	模, 分类: 解析理论; 与模形式的关系[参见32G13]		Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
14J17	奇异性[参见14B05, 14E15]		Singularities [See also 14B05, 14E15]
14J20	算术基域[参见11Dxx, 11G25, 11G35, 14Gxx]		Arithmetic ground fields [See also 11Dxx, 11G25, 11G35, 14Gxx]
14J25	特殊曲面(Hilbert模曲面, 见14G35)		Special surfaces (For Hilbert modular surfaces, see 14G35)
14J26	有理曲面和直纹面		Rational and ruled surfaces
14J27	椭圆曲面		Elliptic surfaces
14J28	K3曲面和Enriques曲面		K3 surfaces and Enriques surfaces
14J29	一般型曲面		Surfaces of general type
14J30	3维簇[参见32Q25]		3-folds [See also 32Q25]
14J32	Calabi-Yau流形		Calabi-Yau manifolds
14J33	镜对称[参见11G42, 53D37]		Mirror symmetry [See also 11G42, 53D37]
14J35	4维簇		4-folds
14J40	n维簇(n >4)		n-folds (n >4)
14J45	Fano簇		Fano varieties
14J50	曲面的自同构和高维簇		Automorphisms of surfaces and higher-dimensional varieties
14J60	曲面上的向量丛和高维簇及其模[参见14D20, 14F05, 32Lxx]		Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
14J70	超曲面		Hypersurfaces
14J80	曲面的拓扑(Donaldson多项式, Seiberg-Witten不变量)		Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants)
14J81	与物理的关系		Relationships with physics
14J99	其它		None of the above, but in this section
14Kxx	Abel簇和概型		Abelian varieties and schemes
14K02	同种映射		Isogeny
14K05	代数理论		Algebraic theory
14K10	代数模, 分类[参见11G15]		Algebraic moduli, classification [See also 11G15]
14K12	子簇		Subvarieties
14K15	算术基域[参见11Dxx, 11Fxx, 11Gxx, 14Gxx]		Arithmetic ground fields [See also 11Dxx, 11Fxx, 11Gxx, 14Gxx]
14K20	解析理论; Abel积分和微分		Analytic theory; abelian integrals and differentials
14K22	复数乘法[参见11G15]		Complex multiplication [See also 11G15]
14K25	θ函数[参见14H42]		Theta functions [See also 14H42]
14K30	Picard概型, 高阶Jacobi行列式[参见14H40, 32G20]		Picard schemes, higher Jacobians [See also 14H40, 32G20]
14K99	其它		None of the above, but in this section
14Lxx	代数群(线性代数群, 见20Gxx; Lie代数, 见17B45)		Algebraic Groups (For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45)
14L05	形式群, p-可除群[参见55N22]		Formal groups, p-divisible groups [See also 55N22]
14L10	群簇		Group varieties
14L15	群概型		Group schemes
14L17	仿射代数群, 超代数构造[参见17B45, 18D35]		Affine algebraic groups, hyperalgebra constructions [See also 17B45, 18D35]
14L24	几何不变量理论[参见13A50]		Geometric invariant theory [See also 13A50]
14L30	群作用于簇或概型(商)[参见13A50, 14L24]		Group actions on varieties or schemes (quotients) [See also 13A50, 14L24]
14L35	典型群(几何方面)[参见20Gxx, 51N30]		Classical groups (geometric aspects) [See also 20Gxx, 51N30]
14L40	其它代数群(几何方面)		Other algebraic groups (geometric aspects)
14L99	其它		None of the above, but in this section
14Mxx	特殊簇		Special varieties
14M05	由环条件(阶乘, Cohen-Macaulay, 半正规)定义的簇[参见13F45, 13H10]		Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F45, 13H10]
14M06	环绕[参见13C40]		Linkage [See also 13C40]
14M07	低余维问题		Low codimension problems
14M10	完全相交[参见13C40]		Complete intersections [See also 13C40]
14M12	行列式簇[参见13C40]		Determinantal varieties [See also 13C40]
14M15	Grassmann簇, Schubert簇, 旗流形[参见32M10, 51M35]		Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
14M17	齐次空间及其推广[参见32M10, 53C30, 57T15]		Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
14M20	有理和单有理簇[参见14E08]		Rational and unirational varieties [See also 14E08]
14M22	有理连通簇		Rationally connected varieties
14M25	环面簇, Newton多面体[参见52B20]		Toric varieties, Newton polyhedra [See also 52B20]
14M27	紧化; 对称与球形簇		Compactifications; symmetric and spherical varieties
14M30	超簇[参见32C11, 58A50]		Supervarieties [See also 32C11, 58A50]
14M99	其它		None of the above, but in this section
14Nxx	射影几何和枚举几何[参见51-XX]		Projective and enumerative geometry [See also 51-XX]
14N05	射影技巧[参见51N35]		Projective techniques [See also 51N35]
14N10	枚举问题(组合问题)		Enumerative problems (combinatorial problems)
14N15	经典问题, Schubert演算		Classical problems, Schubert calculus
14N20	线性子空间的构形和布局		Configurations and arrangements of linear subspaces
14N25	低度簇		Varieties of low degree
14N30	相伴问题		Adjunction problems
14N35	Gromov-Witten不变量, 量子上同调, Gopakumar-Vafa不变量, Donaldson-Thomas不变量[参见53D45]		Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
14N99	其它		None of the above, but in this section
14Pxx	实代数和实解析几何		Real algebraic and real analytic geometry
14P05	实代数集[参见12D15, 13J30]		Real algebraic sets [See also 12D15, 13J30]
14P10	半代数集和相关空间		Semialgebraic sets and related spaces
14P15	实解析集和半解析集[参见32B20, 32C05]		Real analytic and semianalytic sets [See also 32B20, 32C05]
14P20	Nash函数和流形[参见32C07, 58A07]		Nash functions and manifolds [See also 32C07, 58A07]
14P25	实代数簇的拓扑		Topology of real algebraic varieties
14P99	其它		None of the above, but in this section
14Qxx	代数几何的计算方面[参见12Y05, 13Pxx, 68W30]		Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]
14Q05	曲线		Curves
14Q10	曲面, 超曲面		Surfaces, hypersurfaces
14Q15	高维簇		Higher-dimensional varieties
14Q20	有效性, 复杂性		Effectivity, complexity
14Q99	其它		None of the above, but in this section
14Rxx	仿射几何		Affine geometry
14R05	仿射簇的分类		Classification of affine varieties
14R10	仿射空间(自同构, 嵌入, 异种结构, 消没问题)		Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
14R15	Jacobi问题		Jacobian problem
14R20	在仿射簇上的群作用[参见13A50, 14L30]		Group actions on affine varieties [See also 13A50, 14L30]
14R25	仿射纤维化[参见14D06]		Affine fibrations [See also 14D06]
14R99	其它		None of the above, but in this section
14Txx	Tropical几何[参见12K10, 14M25, 14N10, 52B20]		Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
14T05	Tropical几何[参见12K10, 14M25, 14N10, 52B20]		Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
14T99	其它		None of the above, but in this section
15-XX	线性代数和多重线性代数; 矩阵论		Linear and multilinear algebra; matrix theory
15-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
15-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
15-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
15-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
15-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
15-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
15Axx	基础线性代数		Basic linear algebra
15A03	向量空间, 线性相关, 秩		Vector spaces, linear dependence, rank
15A04	线性变换, 半线性变换		Linear transformations, semilinear transformations
15A06	线性方程		Linear equations
15A09	矩阵反演, 广义逆		Matrix inversion, generalized inverses
15A12	矩阵的条件[参见65F35]		Conditioning of matrices [See also 65F35]
15A15	行列式, 积和式, 其它特殊的矩阵函数[参见19B10, 19B14]		Determinants, permanents, other special matrix functions [See also 19B10, 19B14]
15A16	矩阵指数与矩阵相似函数		Matrix exponential and similar functions of matrices
15A18	特征值, 奇异值和特征向量		Eigenvalues, singular values, and eigenvectors
15A21	标准型, 约化, 分类		Canonical forms, reductions, classification
15A22	矩阵束[参见47A56]		Matrix pencils [See also 47A56]
15A23	矩阵的因式分解		Factorization of matrices
15A24	矩阵方程和恒等式		Matrix equations and identities
15A27	交换性		Commutativity
15A29	逆问题		Inverse problems
15A30	矩阵的代数系统[参见16S50, 20Gxx, 20Hxx]		Algebraic systems of matrices [See also 16S50, 20Gxx, 20Hxx]
15A33	特殊环上的矩阵(四元数、有限域等)		Matrices over special rings (quaternions, finite fields, etc.)
15A39	线性不等式		Linear inequalities
15A42	涉及特征值和特征向量的不等式		Inequalities involving eigenvalues and eigenvectors
15A45	各种涉及矩阵的不等式		Miscellaneous inequalities involving matrices
15A54	一个或多个变量函数环上的矩阵		Matrices over function rings in one or more variables
15A60	矩阵的范数, 数值范围, 泛函分析在矩阵论中的应用[参见65F35, 65J05]		Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
15A63	二次型和双线性型, 内积[主要见11Exx]		Quadratic and bilinear forms, inner products [See mainly 11Exx]
15A66	Clifford代数, 旋量		Clifford algebras, spinors
15A69	多重线性代数, 张量积		Multilinear algebra, tensor products
15A72	向量和张量代数, 不变量理论[参见13A50, 14L24]		Vector and tensor algebra, theory of invariants [See also 13A50, 14L24]
15A75	外代数, Grassmann代数		Exterior algebra, Grassmann algebras
15A78	用模构建的其它代数		Other algebras built from modules
15A80	最大加与相关代数		Max-plus and related algebras
15A83	矩阵完备化问题		Matrix completion problems
15A86	线性保持问题		Linear preserver problems
15A99	杂题		Miscellaneous topics
15Bxx	特殊矩阵		Special matrices
15B05	Toeplitz, Cauchy及其相关矩阵		Toeplitz, Cauchy, and related matrices
15B10	正交矩阵		Orthogonal matrices
15B15	模糊矩阵		Fuzzy matrices
15B33	特殊环上的矩阵(四元数、有限域等)		Matrices over special rings (quaternions, finite fields, etc.)
15B34	Boole和Hadamard矩阵		Boolean and Hadamard matrices
15B35	符号模式矩阵		Sign pattern matrices
15B36	整数矩阵[参见11C20]		Matrices of integers [See also 11C20]
15B48	正矩阵及其推广; 矩阵锥		Positive matrices and their generalizations; cones of matrices
15B51	随机矩阵		Stochastic matrices
15B52	随机矩阵		Random matrices
15B57	Hermitian, 斜-Hermitian及其相关矩阵		Hermitian, skew-Hermitian, and related matrices
15B99	其它		None of the above, but in this section
16-XX	结合环与结合代数(交换情形, 见13-XX)		Associative rings and algebras (For the commutative case, see 13-XX)
16-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
16-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
16-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
16-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
16-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
16-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
16Bxx	一般问题与杂题		General and miscellaneous
16B50	范畴论的方法和结果(16D90除外)[参见18-XX]		Category-theoretic methods and results (except as in 16D90) [See also 18-XX]
16B70	逻辑应用[参见03Cxx]		Applications of logic [See also 03Cxx]
16B99	其它		None of the above, but in this section
16Dxx	模, 双模和理想		Modules, bimodules and ideals
16D10	一般模理论		General module theory
16D20	双模		Bimodules
16D25	理想		Ideals
16D30	无穷维单环(16Kxx除外)		Infinite-dimensional simple rings (except as in 16Kxx)
16D40	自由模, 射影模和平坦模及理想[参见19A13]		Free, projective, and flat modules and ideals [See also 19A13]
16D50	内射模, 自内射环[参见16L60]		Injective modules, self-injective rings [See also 16L60]
16D60	单模和半单模, 本原环和理想		Simple and semisimple modules, primitive rings and ideals
16D70	结构和分类(16Gxx除外), 直和分解, 消去		Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
16D80	模和理想的其它类[参见16G50]		Other classes of modules and ideals [See also 16G50]
16D90	模范畴[参见16Gxx, 16S90]; 范畴论中的模理论; Morita等价与对偶		Module categories [See also 16Gxx, 16S90]; module theory in a category-theoretic context; Morita equivalence and duality
16D99	其它		None of the above, but in this section
16Exx	同调方法(交换环, 见13Dxx; 一般范畴, 见18Gxx)		Homological methods (For commutative rings, see 13Dxx; for general categories, see 18Gxx)
16E05	合冲, 预解, 复形		Syzygies, resolutions, complexes
16E10	同调维数		Homological dimension
16E20	Grothendieck群、K-理论等[参见18F30, 19Axx, 19D50]		Grothendieck groups, K-theory, etc. [See also 18F30, 19Axx, 19D50]
16E30	模上的同调函子(Tor、Ext等)		Homological functors on modules (Tor, Ext, etc.)
16E35	导出范畴		Derived categories
16E40	环和代数的(上)同调(例如: Hochschild、循环、二面体等)		(Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
16E45	微分分次代数及其应用		Differential graded algebras and applications
16E50	von Neumann正则环及其推广		von Neumann regular rings and generalizations
16E60	半遗传环和遗传环、自由理想环、Sylvester环等		Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.
16E65	环上的同调条件(正则、Gorenstein、Cohen-Macaulay等环的推广)		Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)
16E99	其它		None of the above, but in this section
16Gxx	环和代数的表示理论		Representation theory of rings and algebras
16G10	Artin环的表示		Representations of Artinian rings
16G20	箭图和偏序集的表示		Representations of quivers and partially ordered sets
16G30	交换环上的整环, 格和代数的表示[参见16Hxx]		Representations of orders, lattices, algebras over commutative rings [See also 16Hxx]
16G50	Cohen-Macaulay模		Cohen-Macaulay modules
16G60	表示类型(有限、驯顺、非驯顺等)		Representation type (finite, tame, wild, etc.)
16G70	Auslander-Reiten序列(几乎分裂序列)与Auslander-Reiten箭图		Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G99	其它		None of the above, but in this section
16Hxx	代数与整环(算术方面, 见11R52, 11R54, 11S45;表示理论, 见16G30)		Algebras and orders (For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30)
16H05	可分代数(例如: 四元数代数、Azumaya代数等)		Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16H10	可分代数的整环		Orders in separable algebras
16H15	交换整环		Commutative orders
16H20	整环上的格		Lattices over orders
16H99	其它		None of the above, but in this section
16Kxx	除环与半单Artin环[参见12E15, 15A30]		Division rings and semisimple Artin rings [See also 12E15, 15A30]
16K20	有限维的(叉积, 见16S35)		Finite-dimensional (For crossed products, see 16S35)
16K40	无限维的与一般情形		Infinite-dimensional and general
16K50	Brauer群[参见12G05, 14F22]		Brauer groups [See also 12G05, 14F22]
16K99	其它		None of the above, but in this section
16Lxx	局部环及其推广		Local rings and generalizations
16L30	非交换局部环和半局部环, 完美环		Noncommutative local and semilocal rings, perfect rings
16L60	拟Frobenius环[参见16D50]		Quasi-Frobenius rings [See also 16D50]
16L99	其它		None of the above, but in this section
16Nxx	环的根和根性质		Radicals and radical properties of rings
16N20	Jacobson根, 拟乘法		Jacobson radical, quasimultiplication
16N40	零和幂零根, 集合, 理想与环		Nil and nilpotent radicals, sets, ideals, rings
16N60	素环与半素环[参见16D60, 16U10]		Prime and semiprime rings [See also 16D60, 16U10]
16N80	广义根和环(模范畴中的根, 见16S90)		General radicals and rings (For radicals in module categories, see 16S90)
16N99	其它		None of the above, but in this section
16Pxx	链条件, 增长条件和其它有限性形式		Chain conditions, growth conditions, and other forms of finiteness
16P10	有限环和有限维代数(半单情形, 见16K20; 交换情形, 见11Txx, 13Mxx)		Finite rings and finite-dimensional algebras (For semisimple, see 16K20; for commutative, see 11Txx, 13Mxx)
16P20	Artin环和模		Artinian rings and modules
16P40	Noether环和模		Noetherian rings and modules
16P50	局部化与Noether环[参见16U20]		Localization and Noetherian rings [See also 16U20]
16P60	零化子与直和项上的链条件: Goldie型条件[参见16U20], Krull维		Chain conditions on annihilators and summands: Goldie-type conditions [See also 16U20], Krull dimension
16P70	其它子模、理想、子环等上的链条件; 凝聚		Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence
16P90	增长率, Gelfand-Kirillov维数		Growth rate, Gelfand-Kirillov dimension
16P99	其它		None of the above, but in this section
16Rxx	具有多项式恒等式的环		Rings with polynomial identity
16R10	T理想, 恒等式, 环与代数的簇		T-ideals, identities, varieties of rings and algebras
16R20	半素多项式恒等式环, 交换环上矩阵中的环可嵌入		Semiprime p.i. rings, rings embeddable in matrices over commutative rings
16R30	迹环与不变量理论		Trace rings and invariant theory
16R40	交换环上矩阵恒等式以外的恒等式		Identities other than those of matrices over commutative rings
16R50	其它恒等式(广义多项式, 有理的, 对合)		Other kinds of identities (generalized polynomial, rational, involution)
16R60	泛函恒等式		Functional identities
16R99	其它		None of the above, but in this section
16Sxx	各种构造下的环与代数		Rings and algebras arising under various constructions
16S10	由泛性质确定的环(自由代数、余积、逆的附加等)		Rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
16S15	有限生成, 有限表示, 范式(菱形引理, 项重写)		Finite generation, finite representability, normal forms (diamond lemma, term-rewriting)
16S20	中心化与正规扩张		Centralizing and normalizing extensions
16S30	Lie代数的泛包络代数[主要见17B35]		Universal enveloping algebras of Lie algebras [See mainly 17B35]
16S32	微分算子环[参见13N10, 32C38]		Rings of differential operators [See also 13N10, 32C38]
16S34	群环[参见20C05, 20C07], Laurent多项式环		Group rings [See also 20C05, 20C07], Laurent polynomial rings
16S35	挠群环和斜群环, 叉积		Twisted and skew group rings, crossed products
16S36	普通多项式环和斜多项式环以及半群环[参见20M25]		Ordinary and skew polynomial rings and semigroup rings [See also 20M25]
16S37	二次和Koszul代数		Quadratic and Koszul algebras
16S38	来自非交换代数几何的环[参见14A22]		Rings arising from non-commutative algebraic geometry [See also 14A22]
16S40	一般Hopf作用的Smash积[参见16T05]		Smash products of general Hopf actions [See also 16T05]
16S50	自同态环; 矩阵环[参见15-XX]		Endomorphism rings; matrix rings [See also 15-XX]
16S60	函数环, 子直积, 环层		Rings of functions, subdirect products, sheaves of rings
16S70	用理想表示的环扩张		Extensions of rings by ideals
16S80	环形变[参见13D10, 14D15]		Deformations of rings [See also 13D10, 14D15]
16S85	分式环与局部化[参见13B30]		Rings of fractions and localizations [See also 13B30]
16S90	挠理论; 模范畴上的根[参见13D30, 18E40](环的根, 见16Nxx)		Torsion theories; radicals on module categories [See also 13D30, 18E40](For radicals of rings, see 16Nxx)
16S99	其它		None of the above, but in this section
16Txx	Hopf代数, 量子群及相关课题		Hopf algebras, quantum groups and related topics
16T05	Hopf代数及其应用[参见16S40, 57T05]		Hopf algebras and their applications [See also 16S40, 57T05]
16T10	双代数		Bialgebras
16T15	余代数与余模;余环		Coalgebras and comodules; corings
16T20	量子群的环论方面[参见17B37, 20G42, 81R50]		Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
16T25	Yang-Baxter方程		Yang-Baxter equations
16T30	与组合学的联系		Connections with combinatorics
16T99	其它		None of the above, but in this section
16Uxx	元素的条件		Conditions on elements
16U10	整环		Integral domains
16U20	Ore环, 乘性集, Ore局部化		Ore rings, multiplicative sets, Ore localization
16U30	可除性, 非交换惟一因式分解整环		Divisibility, noncommutative UFDs
16U60	单位, 单位群		Units, groups of units
16U70	中心, 正规化子(不变元)		Center, normalizer (invariant elements)
16U80	交换性的推广		Generalizations of commutativity
16U99	其它		None of the above, but in this section
16Wxx	具有附加结构的环和代数		Rings and algebras with additional structure
16W10	具有对合的环; Lie结构, Jordan结构和其它非结合结构[参见17B60, 17C50, 46Kxx]		Rings with involution; Lie, Jordan and other nonassociative structures [See also 17B60, 17C50, 46Kxx]
16W20	自同构与自同态		Automorphisms and endomorphisms
16W22	群和半群的作用; 不变量理论		Actions of groups and semigroups; invariant theory
16W25	求导, Lie代数的作用		Derivations, actions of Lie algebras
16W50	分次环与分次模		Graded rings and modules
16W55	“超”(或“斜”)结构[参见17A70, 17Bxx, 17C70](外代数, 见15A75; Clifford代数, 见11E88, 15A66)		“Super” (or “skew”) structure [See also 17A70, 17Bxx, 17C70] (For exterior algebras, see 15A75; for Clifford algebras, see 11E88, 15A66)
16W60	赋值, 完备性, 形式幂级数和相关构造[参见13Jxx]		Valuations, completions, formal power series and related constructions [See also 13Jxx]
16W70	滤子化环; 过滤和分次技巧		Filtered rings; filtrational and graded techniques
16W80	拓扑环和有序环及模[参见06F25, 13Jxx]		Topological and ordered rings and modules [See also 06F25, 13Jxx]
16W99	其它		None of the above, but in this section
16Yxx	推广(非结合环, 见17-XX)		Generalizations (For nonassociative rings, see 17-XX)
16Y30	拟环[参见12K05]		Near-rings [See also 12K05]
16Y60	半环[参见12K10]		Semirings [See also 12K10]
16Y99	其它		None of the above, but in this section
16Zxx	结合环的计算方面		Computational aspects of associative rings
16Z05	结合环的计算方面[参见68W30]		Computations aspects of associative rings [See also 68W30]
16Z99	其它		None of the above, but in this section
17-XX	非结合环与非结合代数		Nonassociative rings and algebras
17-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
17-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
17-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
17-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
17-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
17-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
17-08	计算方法		Computational methods
17Axx	一般非结合环		General nonassociative rings
17A01	一般理论		General theory
17A05	幂结合环		Power-associative rings
17A15	非交换Jordan代数		Noncommutative Jordan algebras
17A20	可拐代数		Flexible algebras
17A30	满足其它恒等式的代数		Algebras satisfying other identities
17A32	Leibniz代数		Leibniz algebras
17A35	可除代数		Division algebras
17A36	自同构, 求导, 其它算子		Automorphisms, derivations, other operators
17A40	三元合成		Ternary compositions
17A42	其它n元合成(n≥3)		Other n-ary compositions (n≥3)
17A45	二次代数(非二次Jordan代数)		Quadratic algebras (but not quadratic Jordan algebras)
17A50	自由代数		Free algebras
17A60	结构理论		Structure theory
17A65	根理论		Radical theory
17A70	超代数		Superalgebras
17A75	合成代数		Composition algebras
17A80	赋值代数		Valued algebras
17A99	其它		None of the above, but in this section
17Bxx	Lie代数和Lie超代数(Lie群, 见22Exx)		Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
17B01	恒等式, 自由Lie(超)代数		Identities, free Lie (super) algebras
17B05	结构理论		Structure theory
17B08	余伴随轨道; 幂零簇		Coadjoint orbits; nilpotent varieties
17B10	表示, 代数理论(权)		Representations, algebraic theory (weights)
17B15	表示, 解析理论		Representations, analytic theory
17B20	单, 半单, 约化(超)代数		Simple, semisimple, reductive (super) algebras
17B22	根系		Root systems
17B25	例外(超)代数		Exceptional (super)algebras
17B30	可解代数, 幂零(超)代数		Solvable, nilpotent (super) algebras
17B35	泛包络(超)代数[参见16S30]		Universal enveloping (super) algebras [See also 16S30]
17B37	量子群(量子包络代数)和有关形变[参见16T20, 20G42, 81R50, 82B23]		Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
17B40	自同构, 求导, 其它算子		Automorphisms, derivations, other operators
17B45	线性代数群的Lie代数[参见14Lxx和20Gxx]		Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx]
17B50	模Lie(超)代数		Modular Lie (super) algebras
17B55	Lie(超)代数中的同调方法		Homological methods in Lie (super)algebras
17B56	Lie(超)代数的上同调		Cohomology of Lie (super) algebras
17B60	伴有其它结构(结合的、Jordan等)的Lie(超)代数[参见16W10, 17C40, 17C50]		Lie (super) algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50]
17B62	Lie双代数; Lie余代数		Lie bialgebras; Lie coalgebras
17B63	Poisson代数		Poisson algebras
17B65	无限维Lie(超)代数[参见22E65]		Infinite-dimensional Lie (super) algebras [See also 22E65]
17B66	向量域Lie(超)代数与有关的(超)代数		Lie algebras of vector fields and related (super) algebras
17B67	Kac-Moody(超)代数; 扩展的仿射Lie代数; 环形Lie代数		Kac-Moody (super) algebras; extended affine Lie algebras; toroidal Lie algebras
17B68	Virasoro代数和相关代数		Virasoro and related algebras
17B69	极点算子; 极点算子代数和相关结构		Vertex operators; vertex operator algebras and related structures
17B70	分次Lie(超)代数		Graded Lie (super) algebras
17B75	着色Lie(超)代数		Color Lie (super) algebras
17B80	应用于可积系统		Applications to integrable systems
17B81	应用于物理		Applications to physics
17B99	其它		None of the above, but in this section
17Cxx	Jordan代数(代数, 三元组和对)		Jordan algebras (algebras, triples and pairs)
17C05	恒等式与自由Jordan结构		Identities and free Jordan structures
17C10	结构理论		Structure theory
17C17	根		Radicals
17C20	单, 半单代数		Simple, semisimple algebras
17C27	幂等的, Peirce分解		Idempotents, Peirce decompositions
17C30	结合群, 自同构		Associated groups, automorphisms
17C36	结合流形		Associated manifolds
17C37	结合几何		Associated geometries
17C40	例外Jordan结构		Exceptional Jordan structures
17C50	具有其它结构的Jordan结构[参见16W10]		Jordan structures associated with other structures [See also 16W10]
17C55	有限维结构		Finite-dimensional structures
17C60	可除代数		Division algebras
17C65	Banach空间和代数上的Jordan结构[参见46H70, 46L70]		Jordan structures on Banach spaces and algebras [See also 46H70, 46L70]
17C70	超结构		Super structures
17C90	应用于物理		Applications to physics
17C99	其它		None of the above, but in this section
17Dxx	其它非结合环与代数		Other nonassociative rings and algebras
17D05	交错环		Alternative rings
17D10	Mal'cev(Mal'tsev)环与代数		Mal'cev (Mal'tsev) rings and algebras
17D15	右交错环		Right alternative rings
17D20	(γ, δ)-环, 包含(1, －1)-环		(γ, δ)-rings, including (1, －1)-rings
17D25	Lie容许代数		Lie-admissible algebras
17D92	遗传代数		Genetic algebras
17D99	其它		None of the above, but in this section
18-XX	范畴论; 同调代数(交换环, 见13Dxx;结合环16Exx, 群20Jxx, 拓扑群和相关结构57Txx; 代数拓扑, 参见55Nxx和55Uxx)		Category theory; homological algebra (For commutative rings see 13Dxx, for associative rings 16Exx, for groups 20Jxx, for topological groups and related structures 57Txx see also 55Nxx and 55Uxx for algebraic topology)
18-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
18-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
18-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
18-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
18-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
18-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
18Axx	范畴与函子的一般理论		General theory of categories and functors
18A05	定义与推广		Definitions, generalizations
18A10	图, 图解概型, 预范畴[特别见20L05]		Graphs, diagram schemes, precategories [See especially 20L05]
18A15	基础, 与逻辑和演绎系统的关系[参见03-XX]		Foundations, relations to logic and deductive systems [See also 03-XX]
18A20	满射, 单射, 特殊类射, 零射		Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
18A22	函子的特性(忠实的、满的等)		Special properties of functors (faithful, full, etc.)
18A23	自然射, 双自然射		Natural morphisms, dinatural morphisms
18A25	函子范畴, 逗号范畴		Functor categories, comma categories
18A30	极限与上极限(积、和、有向极限、前推、纤维积、等化子、核、端和上端等)		Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
18A32	射的因子分解, 子结构, 商结构, 同余, 融和		Factorization of morphisms, substructures, quotient structures, congruences, amalgams
18A35	容许极限范畴(完全范畴), 保极限函子, 完备化		Categories admitting limits (complete categories), functors preserving limits, completions
18A40	伴随函子(泛构造、反射子范畴、Kan扩张等)		Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
18A99	其它		None of the above, but in this section
18Bxx	特殊范畴		Special categories
18B05	集范畴, 特征[参见03-XX]		Category of sets, characterizations [See also 03-XX]
18B10	关系范畴, 加法关系		Category of relations, additive relations
18B15	嵌入定理, 泛范畴[参见18E20]		Embedding theorems, universal categories [See also 18E20]
18B20	机器范畴, 自动机, 运算范畴[参见03D05, 68Qxx]		Categories of machines, automata, operative categories [See also 03D05, 68Qxx]
18B25	普通概念[参见03G30]		Topoi [See also 03G30]
18B30	拓扑空间的范畴与连续映射[参见54-XX]		Categories of topological spaces and continuous mappings [See also 54-XX]
18B35	前序, 序和格(被视作范畴)[参见06-XX]		Preorders, orders and lattices (viewed as categories) [See also 06-XX]
18B40	广群, 半广群, 半群, 群(被视作范畴)[参见20Axx, 20L05, 20Mxx]		Groupoids, semigroupoids, semigroups, groups (viewed as categories) [See also 20Axx, 20L05, 20Mxx]
18B99	其它		None of the above, but in this section
18Cxx	范畴与理论		Categories and theories
18C05	等价范畴[参见03C05, 08C05]		Equational categories [See also 03C05, 08C05]
18C10	理论(例如: 代数理论), 结构和语义学[参见03G30]		Theories (e.g. algebraic theories), structure, and semantics [See also 03G30]
18C15	三元组(=标准构造, 一元或三元组), 三元组代数, 同调与三元组导出函子[参见18Gxx]		Triples (= standard construction, monad or triad), algebras for a triple, homology and derived functors for triples [See also 18Gxx]
18C20	与一元组相伴的代数和Kleisli范畴		Algebras and Kleisli categories associated with monads
18C30	梗概及其推广		Sketches and generalizations
18C35	可达和局部有规矩范畴		Accessible and locally presentable categories
18C50	形式语言的范畴语义学[参见68Q55, 68Q65]		Categorical semantics of formal languages [See also 68Q55, 68Q65]
18C99	其它		None of the above, but in this section
18Dxx	有结构的范畴		Categories with structure
18D05	双重范畴, 2范畴, 双范畴及其推广		Double categories, 2-categories, bicategories and generalizations
18D10	单项范畴(=乘法范畴), 对称单项范畴, 辫范畴[参见19D23]		Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories [See also 19D23]
18D15	闭范畴(闭单项范畴和Descartes闭范畴等)		Closed categories (closed monoidal and Cartesian closed categories, etc.)
18D20	浓缩范畴(闭范畴或单项范畴之上)		Enriched categories (over closed or monoidal categories)
18D25	强函子, 强附加		Strong functors, strong adjunctions
18D30	纤维范畴		Fibered categories
18D35	范畴中的结构化对象(群对象等)		Structured objects in a category (group objects, etc.)
18D50	Operads[参见55P48]		Operads [See also 55P48]
18D99	其它		None of the above, but in this section
18Exx	Abel范畴		Abelian categories
18E05	预加性范畴, 加法范畴		Preadditive, additive categories
18E10	正合范畴, Abel范畴		Exact categories, abelian categories
18E15	Grothendieck范畴		Grothendieck categories
18E20	嵌入定理[参见18B15]		Embedding theorems [See also 18B15]
18E25	导出函子和卫星		Derived functors and satellites
18E30	导出范畴, 三角范畴		Derived categories, triangulated categories
18E35	范畴的局部化		Localization of categories
18E40	挠理论, 根[参见13D30, 16S90]		Torsion theories, radicals [See also 13D30, 16S90]
18E99	其它		None of the above, but in this section
18Fxx	范畴与几何		Categories and geometry
18F05	局部范畴与函子		Local categories and functors
18F10	Grothendieck拓扑[参见14F20]		Grothendieck topologies [See also 14F20]
18F15	抽象流形与纤维丛[参见55Rxx, 57Pxx]		Abstract manifolds and fiber bundles [See also 55Rxx, 57Pxx]
18F20	预层和层[参见14F05, 32C35, 32L10, 54B40, 55N30]		Presheaves and sheaves [See also 14F05, 32C35, 32L10, 54B40, 55N30]
18F25	代数K-理论与L-理论[参见11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]		Algebraic K-theory and L-theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
18F30	Grothendieck群[参见13D15, 16E20, 19Axx]		Grothendieck groups [See also 13D15, 16E20, 19Axx]
18F99	其它		None of the above, but in this section
18Gxx	同调代数[参见13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]		Homological algebra [See also 13Dxx, 16Exx, 20Jxx, 55Nxx, 55Uxx, 57Txx]
18G05	射影与内射[参见13C10, 13C11, 16D40, 16D50]		Projectives and injectives [See also 13C10, 13C11, 16D40, 16D50]
18G10	预解; 导出函子[参见13D02, 16E05, 18E25]		Resolutions; derived functors [See also 13D02, 16E05, 18E25]
18G15	Ext与Tor, 推广, Künneth公式[参见55U25]		Ext and Tor, generalizations, Künneth formula [See also 55U25]
18G20	同调维数[参见13D05, 16E10]		Homological dimension [See also 13D05, 16E10]
18G25	相关同调代数, 射影类		Relative homological algebra, projective classes
18G30	单纯集, 单纯对象(在一个范畴中)[参见55U10]		Simplicial sets, simplicial objects (in a category) [See also 55U10]
18G35	链复形[参见18E30, 55U15]		Chain complexes [See also 18E30, 55U15]
18G40	谱序列, 超上同调[参见55Txx]		Spectral sequences, hypercohomology [See also 55Txx]
18G50	非Abel同调代数		Nonabelian homological algebra
18G55	同伦代数		Homotopical algebra
18G60	其它(上)同调理论[参见19D55, 46L80, 58J20, 58J22]		Other (co)homology theories [See also 19D55, 46L80, 58J20, 58J22]
18G99	其它		None of the above, but in this section
19-XX	K-理论[参见16E20, 18F25]		K-theory [See also 16E20, 18F25]
19-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
19-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
19-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
19-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
19-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
19-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
19Axx	Grothendieck群和K₀[参见13D15, 18F30]		Grothendieck groups and K₀[See also 13D15, 18F30]
19A13	射影模的稳定性[参见13C10]		Stability for projective modules [See also 13C10]
19A15	有效生成		Efficient generation
19A22	Frobenius归纳法, Burnside环与表示环		Frobenius induction, Burnside and representation rings
19A31	群环和整环的K₀		K₀ of group rings and orders
19A49	其它环的K₀		K₀ of other rings
19A99	其它		None of the above, but in this section
19Bxx	Whitehead群和K₁		Whitehead groups and K₁
19B10	稳定区域条件		Stable range conditions
19B14	线性群的稳定性		Stability for linear groups
19B28	群环和整环的K₁[参见57Q10]		K₁ of group rings and orders [See also 57Q10]
19B37	同余子群问题[参见20H05]		Congruence subgroup problems [See also 20H05]
19B99	其它		None of the above, but in this section
19Cxx	Steinberg群和K₂		Steinberg groups and K₂
19C09	中心扩张与Schur乘子		Central extensions and Schur multipliers
19C20	K₂的符号, 表达式和稳定性		Symbols, presentations and stability of K₂
19C30	K₂和Brauer群		K₂ and the Brauer group
19C40	K₂的分割		Excision for K₂
19C99	其它		None of the above, but in this section
19Dxx	高等代数K-理论		Higher algebraic K-theory
19D06	Q-构造和附加构造		Q- and plus-constructions
19D10	空间的代数K-理论		Algebraic K-theory of spaces
19D23	对称单项范畴[参见18D10]		Symmetric monoidal categories [See also 18D10]
19D25	Karoubi-Villamayor-Gersten K-理论		Karoubi-Villamayor-Gersten K-theory
19D35	负K-理论, NK与幂零		Negative K-theory, NK and Nil
19D45	高等符号, Milnor K-理论		Higher symbols, Milnor K-theory
19D50	环的高等K-理论的计算[参见13D15, 16E20]		Computations of higher K-theory of rings [See also 13D15, 16E20]
19D55	K-理论与同调; 循环同调与上同调[参见18G60]		K-theory and homology; cyclic homology and cohomology [See also 18G60]
19D99	其它		None of the above, but in this section
19Exx	几何中的K-理论		K-theory in geometry
19E08	概型的K-理论[参见14C35]		K-theory of schemes [See also 14C35]
19E15	代数闭链和主上同调[参见14C25, 14C35]		Algebraic cycles and motivic cohomology [See also 14C25, 14C35]
19E20	与上同调理论的关系[参见14Fxx]		Relations with cohomology theories [See also 14Fxx]
19E99	其它		None of the above, but in this section
19Fxx	数论中的K-理论[参见11R70, 11S70]		K-theory in number theory [See also 11R70, 11S70]
19F05	一般类域理论[参见11G45]		Generalized class field theory [See also 11G45]
19F15	符号与算术[参见11R37]		Symbols and arithmetic [See also 11R37]
19F27	Étale上同调, 高等调节器, ζ函数和L-函数[参见11G40, 11R42, 11S40, 14F20, 14G10]		Étale cohomology, higher regulators, zeta and L-functions [See also 11G40, 11R42, 11S40, 14F20, 14G10]
19F99	其它		None of the above, but in this section
19Gxx	型的K-理论[参见11Exx]		K-theory of forms [See also 11Exx]
19G05	二次模的稳定性		Stability for quadratic modules
19G12	环的Witt群[参见11E81]		Witt groups of rings [See also 11E81]
19G24	群环的L-理论[参见11E81]		L-theory of group rings [See also 11E81]
19G38	Hermite K-理论, 与环的K-理论的关系		Hermitian K-theory, relations with K-theory of rings
19G99	其它		None of the above, but in this section
19Jxx	来自拓扑的障碍		Obstructions from topology
19J05	K₀中的有限性和其它障碍		Finiteness and other obstructions in K₀
19J10	Whitehead(和有关的)挠		Whitehead (and related) torsion
19J25	换球术障碍[参见57R67]		Surgery obstructions [See also 57R67]
19J35	群作用的障碍		Obstructions to group actions
19J99	其它		None of the above, but in this section
19Kxx	K-理论与算子代数[主要见46L80, 46M20]		K-theory and operator algebras [See mainly 46L80, and also 46M20]
19K14	作为有序群的K₀, 迹		K₀ as an ordered group, traces
19K33	EXT与K-同调[参见55N22]		EXT and K-homology [See also 55N22]
19K35	Kasparov(KK-理论)[参见58J22]		Kasparov theory (KK-theory) [See also 58J22]
19K56	指标理论[参见58J20, 58J22]		Index theory [See also 58J20, 58J22]
19K99	其它		None of the above, but in this section
19Lxx	拓扑K-理论[参见55N15, 55R50, 55S25]		Topological K-theory [See also 55N15, 55R50, 55S25]
19L10	Riemann-Roch定理, Chern特征标		Riemann-Roch theorems, Chern characters
19L20	J-同态, Adams运算[参见55Q50]		J-homomorphism, Adams operations [See also 55Q50]
19L41	连通K-理论, 配边[参见55N22]		Connective K-theory, cobordism [See also 55N22]
19L47	等变K-理论[参见55N91, 55P91, 55Q91, 55R91, 55S91]		Equivariant K-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]
19L50	扭K-理论;微分K-理论		Twisted K-theory; differential K-theory
19L64	计算, 几何应用		Computations, geometric applications
19L99	其它		None of the above, but in this section
19Mxx	K-理论的各种应用		Miscellaneous applications of K-theory
19M05	K-理论的各种应用		Miscellaneous applications of K-theory
19M99	其它		None of the above, but in this section
20-XX	群论及其推广		Group theory and generalizations
20-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
20-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
20-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
20-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
20-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
20-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
20Axx	基础		Foundations
20A05	公理系统与基本性质		Axiomatics and elementary properties
20A10	元数学的考虑(字问题, 见20F10)		Metamathematical considerations (For word problems, see 20F10)
20A15	逻辑在群论中的应用		Applications of logic to group theory
20A99	其它		None of the above, but in this section
20Bxx	置换群		Permutation groups
20B05	有限群的一般理论		General theory for finite groups
20B07	无限群的一般理论		General theory for infinite groups
20B10	特征定理		Characterization theorems
20B15	本原群		Primitive groups
20B20	多重可迁有限群		Multiply transitive finite groups
20B22	多重可迁无限群		Multiply transitive infinite groups
20B25	代数, 几何或组合结构的有限自同构群[参见05Bxx, 12F10, 20G40, 20H30, 51-XX]		Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]
20B27	无限自同构群[参见12F10]		Infinite automorphism groups [See also 12F10]
20B30	对称群		Symmetric groups
20B35	对称群的子群		Subgroups of symmetric groups
20B40	计算方法		Computational methods
20B99	其它		None of the above, but in this section
20Cxx	群表示理论[参见19A22(表示环和Burnside环)]		Representation theory of groups [See also 19A22 (for representation rings and Burnside rings)]
20C05	有限群的群环及其模[参见16S34]		Group rings of finite groups and their modules [See also 16S34]
20C07	无限群的群环及其模[参见16S34]		Group rings of infinite groups and their modules [See also 16S34]
20C08	Hecke代数及其表示		Hecke algebras and their representations
20C10	有限群的整数表示		Integral representations of finite groups
20C11	有限群的p-进表示		p-adic representations of finite groups
20C12	无限群的整数表示		Integral representations of infinite groups
20C15	一般表示与特征标		Ordinary representations and characters
20C20	模表示与特征标		Modular representations and characters
20C25	射影表示与乘子		Projective representations and multipliers
20C30	有限对称群的表示		Representations of finite symmetric groups
20C32	无限对称群的表示		Representations of infinite symmetric groups
20C33	有限Lie型群的表示		Representations of finite groups of Lie type
20C34	散在群的表示		Representations of sporadic groups
20C35	群表示理论在物理中的应用		Applications of group representations to physics
20C40	计算方法		Computational methods
20C99	其它		None of the above, but in this section
20Dxx	抽象有限群		Abstract finite groups
20D05	有限单群及其分类		Finite simple groups and their classification
20D06	单群: 交错群和Lie型群[参见20Gxx]		Simple groups: alternating groups and groups of Lie type [See also 20Gxx]
20D08	单群: 分散群(零星群)		Simple groups: sporadic groups
20D10	可解群, 形成理论, Schunck类, Fitting类, π-长度, 秩[参见20F17]		Solvable groups, theory of formations, Schunck classes, Fitting classes, π-length, ranks [See also 20F17]
20D15	幂零群, p-群		Nilpotent groups, p-groups
20D20	Sylow群, Sylow性质, π群, π结构		Sylow subgroups, Sylow properties, π-groups, π-structure
20D25	特殊子群(Frattini、Fitting等)		Special subgroups (Frattini, Fitting, etc.)
20D30	子群的列和格		Series and lattices of subgroups
20D35	次正规子群		Subnormal subgroups
20D40	子群的积		Products of subgroups
20D45	自同构		Automorphisms
20D60	算术与组合问题		Arithmetic and combinatorial problems
20D99	其它		None of the above, but in this section
20Exx	无限群或有限群的结构与分类		Structure and classification of infinite or finite groups
20E05	自由非Abel群		Free nonabelian groups
20E06	自由积, 有融合的自由积, Higman-Neumann-Neumann扩张及其推广		Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E07	子群定理; 子群增长性		Subgroup theorems; subgroup growth
20E08	作用于树上的群[参见20F65]		Groups acting on trees [See also 20F65]
20E10	群的拟簇和簇		Quasivarieties and varieties of groups
20E15	子群的链与格, 次正规子群[参见20F22]		Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
20E18	极限, 投射有限群		Limits, profinite groups
20E22	扩张, 环积与其它合成[参见20J05]		Extensions, wreath products, and other compositions [See also 20J05]
20E25	局部性质		Local properties
20E26	剩余性质及其推广; 剩余有限群		Residual properties and generalizations; residually finite groups
20E28	极大子群		Maximal subgroups
20E32	单群[参见20D05]		Simple groups [See also 20D05]
20E34	一般结构定理		General structure theorems
20E36	无限群的自同构(有限群的自同构, 见20D45)		Automorphisms of infinite groups (For automorphisms of finite groups, see 20D45)
20E42	带BN对的群; 造型[参见51E24]		Groups with a BN-pair; buildings [See also 51E24]
20E45	共轭类		Conjugacy classes
20E99	其它		None of the above, but in this section
20Fxx	无限或有限群的特殊方面		Special aspects of infinite or finite groups
20F05	生成元, 关系和预命题		Generators, relations, and presentations
20F06	消去理论; van Kampen图表的应用[参见57M05]		Cancellation theory; application of van Kampen diagrams [See also 57M05]
20F10	字问题, 其它判定问题, 与逻辑和自动机的关系[参见03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]		Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 68Q70]
20F11	有限Morley秩的群[参见03C45, 03C60]		Groups of finite Morley rank [See also 03C45, 03C60]
20F12	换位子演算		Commutator calculus
20F14	导出列, 中心列及其推广		Derived series, central series, and generalizations
20F16	可解群, 超可解群[参见20D10]		Solvable groups, supersolvable groups [See also 20D10]
20F17	群的形成, Fitting类[参见20D10]		Formations of groups, Fitting classes [See also 20D10]
20F18	幂零群[参见20D15]		Nilpotent groups [See also 20D15]
20F19	可解群与幂零群的推广		Generalizations of solvable and nilpotent groups
20F22	用子群链定义的其它群类		Other classes of groups defined by subgroup chains
20F24	FC-群及其推广		FC-groups and their generalizations
20F28	群的自同构群[参见20E36]		Automorphism groups of groups [See also 20E36]
20F29	作为代数系统自同构群的群表示		Representations of groups as automorphism groups of algebraic systems
20F34	基本群及其自同构[参见57M05, 57Sxx]		Fundamental groups and their automorphisms [See also 57M05, 57Sxx]
20F36	辫群; Artin群		Braid groups; Artin groups
20F38	与拓扑或分析有关的其它群		Other groups related to topology or analysis
20F40	结合Lie结构		Associated Lie structures
20F45	Engel条件		Engel conditions
20F50	周期群; 局部有限群		Periodic groups; locally finite groups
20F55	反射群和Coxeter群[参见22E40, 51F15]		Reflection and Coxeter groups [See also 22E40, 51F15]
20F60	有序群[主要见06F15]		Ordered groups [See mainly 06F15]
20F65	几何群论[参见05C25, 20E08, 57Mxx]		Geometric group theory [See also 05C25, 20E08, 57Mxx]
20F67	双曲群和非正曲线群		Hyperbolic groups and nonpositively curved groups
20F69	群的渐近性质		Asymptotic properties of groups
20F70	群上的代数几何; 群上方程		Algebraic geometry over groups; equations over groups
20F99	其它		None of the above, but in this section
20Gxx	线性代数群及相关课题(算术理论, 见11E57, 11H56; 几何理论, 见14Lxx, 22Exx; 表示论中的其它方法, 见15A30, 22E45, 22E46, 22E47, 22E50, 22E55)		Linear algebraic groups and related topics (For arithmetic theory, see 11E57, 11H56; for geometric theory, see 14Lxx, 22Exx; for other methods in representation theory, see 15A30, 22E45, 22E46, 22E47, 22E50, 22E55)
20G05	表示理论		Representation theory
20G07	结构理论		Structure theory
20G10	上同调论		Cohomology theory
20G15	任意域上的线性代数群		Linear algebraic groups over arbitrary fields
20G20	实数, 复数和四元数体上的线性代数群		Linear algebraic groups over the reals, the complexes, the quaternions
20G25	局部域上的线性代数群及其整群		Linear algebraic groups over local fields and their integers
20G30	整体域上的线性代数群及其整群		Linear algebraic groups over global fields and their integers
20G35	赋值向量环和其它环及概型上的线性代数群		Linear algebraic groups over adèles and other rings and schemes
20G40	有限域上的线性代数群		Linear algebraic groups over finite fields
20G41	例外群		Exceptional groups
20G42	量子群(量子函数代数)及其表示[参见16T20, 17B37, 81R50]		Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
20G43	Schur和q-Schur代数		Schur and q-Schur algebras
20G44	Kac-Moody群		Kac-Moody groups
20G45	物理上的应用		Applications to physics
20G99	其它		None of the above, but in this section
20Hxx	其它矩阵群[参见15A30]		Other groups of matrices [See also 15A30]
20H05	么模群, 同余子群[参见11F06, 19B37, 22E40, 51F20]		Unimodular groups, congruence subgroups [See also 11F06, 19B37, 22E40, 51F20]
20H10	Fuchs群及其推广[参见11F06, 22E40, 30F35, 32Nxx]		Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
20H15	其它几何群, 包括结晶体群[参见51-XX, 特别是51F15和82D25]		Other geometric groups, including crystallographic groups [See also 51-XX, especially 51F15, and 82D25]
20H20	域上的其它矩阵群		Other matrix groups over fields
20H25	环上的其它矩阵群		Other matrix groups over rings
20H30	有限域上的其它矩阵群		Other matrix groups over finite fields
20H99	其它		None of the above, but in this section
20Jxx	与同调代数和范畴论的联系		Connections with homological algebra and category theory
20J05	群论中的同调方法		Homological methods in group theory
20J06	群的上同调		Cohomology of groups
20J15	群的范畴		Category of groups
20J99	其它		None of the above, but in this section
20Kxx	Abel群		Abelian groups
20K01	有限Abel群[和集, 见11B13和11P70]		Finite abelian groups [For sumsets, see 11B13 and 11P70]
20K10	挠群, 准素群及其广义准素群		Torsion groups, primary groups and generalized primary groups
20K15	无挠群, 有限秩		Torsion-free groups, finite rank
20K20	无挠群, 无限秩		Torsion-free groups, infinite rank
20K21	混合群		Mixed groups
20K25	直和、直积等		Direct sums, direct products, etc.
20K27	子群		Subgroups
20K30	自同构、同态、自同态等		Automorphisms, homomorphisms, endomorphisms, etc.
20K35	扩张		Extensions
20K40	同调方法与范畴方法		Homological and categorical methods
20K45	拓扑方法[参见22A05, 22B05]		Topological methods [See also 22A05, 22B05]
20K99	其它		None of the above, but in this section
20Lxx	广群(比如: 所有态射是同构的小范畴)(具有单个二元运算的集合, 见20N02; 拓扑广群, 见22A22, 58H05)		Groupoids (i.e. small categories in which all morphisms are isomorphisms) (For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05)
20L05	广群(比如: 所有态射是同构的小范畴)(具有单个二元运算的集合, 见20N02; 拓扑广群, 见22A22, 58H05)		Groupoids (i.e. small categories in which all morphisms are isomorphisms)(For sets with a single binary operation, see 20N02; for topological groupoids, see 22A22, 58H05)
20L99	其它		None of the above, but in this section
20Mxx	半群		Semigroups
20M05	自由半群, 生成元和关系, 字问题		Free semigroups, generators and relations, word problems
20M07	半群的簇和伪簇		Varieties and pseudovarieties of semigroups
20M10	一般结构理论		General structure theory
20M11	根理论		Radical theory
20M12	理想理论		Ideal theory
20M13	幺半群的算术理论		Arithmetic theory of monoids
20M14	交换半群		Commutative semigroups
20M15	半群的映射		Mappings of semigroups
20M17	正则半群		Regular semigroups
20M18	逆半群		Inverse semigroups
20M19	纯正半群		Orthodox semigroups
20M20	变换半群等[参见47D03, 47H20, 54H15]		Semigroups of transformations, etc. [See also 47D03, 47H20, 54H15]
20M25	半群环, 环的乘法半群[参见16S36, 16Y60]		Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60]
20M30	半群的表示; 集上半群的作用		Representation of semigroups; actions of semigroups on sets
20M32	代数幺半群		Algebraic monoids
20M35	自动机理论中的半群、语言学等[参见03D05, 68Q70, 68T50]		Semigroups in automata theory, linguistics, etc. [See also 03D05, 68Q70, 68T50]
20M50	半群与同调代数和范畴论的联系		Connections of semigroups with homological algebra and category theory
20M99	其它		None of the above, but in this section
20Nxx	群的其它推广		Other generalizations of groups
20N02	具有单个二元运算的集合(广群)		Sets with a single binary operation (groupoids)
20N05	圈, 拟群[参见05Bxx]		Loops, quasigroups [See also 05Bxx]
20N10	三元系(堆、半堆、广堆等)		Ternary systems (heaps, semiheaps, heapoids, etc.)
20N15	n-元系(n≥3)		n-ary systems (n≥3)
20N20	超群		Hypergroups
20N25	模糊群[参见03E72]		Fuzzy groups [See also 03E72]
20N99	其它		None of the above, but in this section
20Pxx	群论中的概率方法[参见60Bxx]		Probabilistic methods in group theory [See also 60Bxx]
20P05	群论中的概率方法[参见60Bxx]		Probabilistic methods in group theory [See also 60Bxx]
20P99	其它		None of the above, but in this section
22-XX	拓扑群, Lie群(变换群, 见54H15, 57Sxx, 58-XX; 抽象调和分析, 见43-XX)		Topological groups, Lie groups (For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX)
22-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
22-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
22-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
22-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
22-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
22-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
22Axx	拓扑与微分代数系统(拓扑环和域, 见12Jxx, 13Jxx, 16W80)		Topological and differentiable algebraic systems (For topological rings and fields, see 12Jxx, 13Jxx, 16W80)
22A05	一般拓扑群的结构		Structure of general topological groups
22A10	一般拓扑群上的分析		Analysis on general topological groups
22A15	拓扑半群的结构		Structure of topological semigroups
22A20	拓扑半群上的分析		Analysis on topological semigroups
22A22	拓扑广群(包括可微广群和Lie广群)[参见58H05]		Topological groupoids (including differentiable and Lie groupoids) [See also 58H05]
22A25	一般拓扑群和拓扑半群的表示		Representations of general topological groups and semigroups
22A26	拓扑半格, 拓扑格和应用[参见06B30, 06B35, 06F30]		Topological semilattices, lattices and applications [See also 06B30, 06B35, 06F30]
22A30	其它拓扑代数系统及其表示		Other topological algebraic systems and their representations
22A99	其它		None of the above, but in this section
22Bxx	局部紧Abel群(LCA群)		Locally compact abelian groups (LCA groups)
22B05	LCA群的一般性质和结构		General properties and structure of LCA groups
22B10	LCA群的群代数的结构		Structure of group algebras of LCA groups
22B99	其它		None of the above, but in this section
22Cxx	紧群		Compact groups
22C05	紧群		Compact groups
22C99	其它		None of the above, but in this section
22Dxx	局部紧群及其代数		Locally compact groups and their algebras
22D05	局部紧群的一般性质和结构		General properties and structure of locally compact groups
22D10	局部紧群的酉表示		Unitary representations of locally compact groups
22D12	局部紧群的其它表示		Other representations of locally compact groups
22D15	局部紧群的群代数		Group algebras of locally compact groups
22D20	群代数的表示		Representations of group algebras
22D25	在群表示中的C^-代数和W^-代数[参见46Lxx]		C^-algebras and W^-algebras in relation to group representations [See also 46Lxx]
22D30	诱导表示		Induced representations
22D35	对偶定理		Duality theorems
22D40	群上的遍历理论[参见28Dxx]		Ergodic theory on groups [See also 28Dxx]
22D45	局部紧群的自同构群		Automorphism groups of locally compact groups
22D99	其它		None of the above, but in this section
22Exx	Lie群(Lie群和齐性空间的拓扑, 见57Sxx, 57Txx; 分析方面, 见43A80, 43A85, 43A90)		Lie groups (For the topology of Lie groups and homogeneous spaces, see 57Sxx, 57Txx; for analysis thereon, see 43A80, 43A85, 43A90)
22E05	局部Lie群[参见34-XX, 35-XX, 58H05]		Local Lie groups [See also 34-XX, 35-XX, 58H05]
22E10	复Lie群的一般性质和结构[参见32M05]		General properties and structure of complex Lie groups [See also 32M05]
22E15	实Lie群的一般性质和结构		General properties and structure of real Lie groups
22E20	其它Lie群的一般性质和结构		General properties and structure of other Lie groups
22E25	幂零Lie群与可解Lie群		Nilpotent and solvable Lie groups
22E27	幂零Lie群与可解Lie群的表示(特殊轨道积分、非I型表示等)		Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
22E30	实Lie群与复Lie群上的分析[参见33C80, 43-XX]		Analysis on real and complex Lie groups [See also 33C80, 43-XX]
22E35	p-进Lie群上的分析		Analysis on p-adic Lie groups
22E40	Lie群的离散子群[参见20Hxx, 32Nxx]		Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
22E41	连续上同调[参见57R32, 57Txx, 58H10]		Continuous cohomology [See also 57R32, 57Txx, 58H10]
22E43	Lorentz群的结构与表示		Structure and representation of the Lorentz group
22E45	实域上Lie群与线性代数群的表示:解析方法[纯代数理论, 见20G05]		Representations of Lie and linear algebraic groups over real fields: analytic methods (For the purely algebraic theory, see 20G05)
22E46	半单Lie群及其表示		Semisimple Lie groups and their representations
22E47	Lie群和实代数群的表示: 代数方法(Verma模等)[参见17B10]		Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
22E50	局部域上Lie群和线性代数群的表示[参见20G05]		Representations of Lie and linear algebraic groups over local fields [See also 20G05]
22E55	整体域和赋值向量环上的Lie群和线性代数群的表示[参见20G05]		Representations of Lie and linear algebraic groups over global fields and adèle rings [See also 20G05]
22E57	几何Langlands程序:表示理论方面[参见14D24]		Geometric Langlands program: representation theoretic aspects [See also 14D24]
22E60	Lie群的Lie代数(Lie代数的代数理论, 见17Bxx)		Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
22E65	无限维Lie群及其Lie代数; 一般性质[参见17B65, 58B25, 58H05]		Infinite-dimensional Lie groups and their Lie algebras; general properties [See also 17B65, 58B25, 58H05]
22E66	无限维Lie群的分析和表示		Analysis on and representations of infinite-dimensional Lie groups
22E67	圈群及有关构造, 群论处理[参见58D05]		Loop groups and related constructions, group-theoretic treatment [See also 58D05]
22E70	Lie群在物理上的应用; 显式表示[参见81R05, 81R10]		Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10]
22E99	其它		None of the above, but in this section
22Fxx	非紧变换群		Noncompact transformation groups
22F05	群和伪群作用的一般理论(具有作用空间的拓扑性质, 见57S20)		General theory of group and pseudogroup actions (For topological properties of spaces with an action, see 57S20)
22F10	可测群作用[参见22D40, 28Dxx, 37Axx]		Measurable group actions [See also 22D40, 28Dxx, 37Axx]
22F30	齐性空间(一般作用在流形或保几何结构, 见57M60, 57Sxx; Lie群的离散子群, 特别见22E40)		Homogeneous spaces (For general actions on manifolds or preserving geometrical structures, see 57M60, 57Sxx; for discrete subgroups of Lie groups, see especially 22E40)
22F50	作为其它结构自同构的群		Groups as automorphisms of other structures
22F99	其它		None of the above, but in this section
26-XX	实函数[参见54C30]		Real functions [See also 54C30]
26-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
26-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
26-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
26-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
26-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
26-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
26Axx	一元函数		Functions of one variable
26A03	基础: 极限及其推广, 初等线拓扑		Foundations: limits and generalizations, elementary topology of the line
26A06	一元微积分		One-variable calculus
26A09	初等函数		Elementary functions
26A12	函数增长率, 无穷阶, 慢变函数[参见26A48]		Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]
26A15	连续性及有关问题(连续性模、半连续性模、间断模等)(由Fourier系数确定的性质, 见42A16; 由逼近性确定的性质, 见41A25, 41A27)		Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) (For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27)
26A16	Lipschitz(Hölder)类		Lipschitz (Hölder) classes
26A18	迭代[参见37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]		Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]
26A21	实函数分类; 集合与函数的Baire分类[参见03E15, 28A05, 54C50]		Classification of real functions; Baire classification of sets and functions [See also 03E15, 28A05, 54C50]
26A24	微分法(一元函数): 一般理论, 广义导数, 中值定理[参见28A15]		Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems [See also 28A15]
26A27	不可微性(不可微函数, 不可微点), 不连续导数		Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives
26A30	奇异函数, Cantor函数, 具有其它特殊性质的函数		Singular functions, Cantor functions, functions with other special properties
26A33	分数次导数和分数次积分		Fractional derivatives and integrals
26A36	反微分法		Antidifferentiation
26A39	Denjoy积分和Perron积分, 其它特殊积分		Denjoy and Perron integrals, other special integrals
26A42	Riemann, Stieltjes和Lebesgue型积分[参见28-XX]		Integrals of Riemann, Stieltjes and Lebesgue type [See also 28-XX]
26A45	有界变差函数, 推广		Functions of bounded variation, generalizations
26A46	绝对连续函数		Absolutely continuous functions
26A48	单调函数, 推广		Monotonic functions, generalizations
26A51	凸性, 推广		Convexity, generalizations
26A99	其它		None of the above, but in this section
26Bxx	多元函数		Functions of several variables
26B05	连续性和微分法问题		Continuity and differentiation questions
26B10	隐函数定理, Jacobi行列式, 多元变换		Implicit function theorems, Jacobians, transformations with several variables
26B12	向量函数的微积分		Calculus of vector functions
26B15	积分法: 长度, 面积, 体积[参见28A75, 51M25]		Integration: length, area, volume [See also 28A75, 51M25]
26B20	积分公式(Stokes、Gauss、Green等)		Integral formulas (Stokes, Gauss, Green, etc.)
26B25	凸性, 推广		Convexity, generalizations
26B30	绝对连续函数, 有界变差函数		Absolutely continuous functions, functions of bounded variation
26B35	多元函数的特性、Hölder条件等		Special properties of functions of several variables, Hölder conditions, etc.
26B40	函数的表示和叠加		Representation and superposition of functions
26B99	其它		None of the above, but in this section
26Cxx	多项式, 有理函数		Polynomials, rational functions
26C05	多项式: 解析性质等[参见12Dxx, 12Exx]		Polynomials: analytic properties, etc. [See also 12Dxx, 12Exx]
26C10	多项式: 零点位置[参见12D10, 30C15, 65H05]		Polynomials: location of zeros [See also 12D10, 30C15, 65H05]
26C15	有理函数[参见14Pxx]		Rational functions [See also 14Pxx]
26C99	其它		None of the above, but in this section
26Dxx	不等式(极大函数不等式, 见42B25; 泛函不等式, 见39B72; 概率不等式, 见60E15)		Inequalities (For maximal function inequalities, see 42B25; for functional inequalities, see 39B72; for probabilistic inequalities, see 60E15)
26D05	三角函数与多项式不等式		Inequalities for trigonometric functions and polynomials
26D07	涉及其它类型函数的不等式		Inequalities involving other types of functions
26D10	涉及求导、微分和积分算子的不等式		Inequalities involving derivatives and differential and integral operators
26D15	和、级数和积分不等式		Inequalities for sums, series and integrals
26D20	其它解析不等式		Other analytical inequalities
26D99	其它		None of the above, but in this section
26Exx	杂题[参见58Cxx]		Miscellaneous topics [See also 58Cxx]
26E05	实解析函数[参见32B05, 32C05]		Real-analytic functions [See also 32B05, 32C05]
26E10	C^∞-函数, 拟解析函数[参见58C25]		C^∞-functions, quasi-analytic functions [See also 58C25]
26E15	无限维空间中函数的微积分[参见46G05, 58Cxx]		Calculus of functions on infinite-dimensional spaces [See also 46G05, 58Cxx]
26E20	在无限维空间中取值的函数的微积分[参见46E40, 46G10, 58Cxx]		Calculus of functions taking values in infinite-dimensional spaces [See also 46E40, 46G10, 58Cxx]
26E25	集值函数[参见28B20, 54C60](非光滑分析, 见49J52, 58Cxx, 90Cxx)		Set-valued functions [See also 28B20, 54C60] (For nonsmooth analysis, see 49J52, 58Cxx, 90Cxx)
26E30	非Archimedes分析[参见12J25]		Non-Archimedean analysis [See also 12J25]
26E35	非标准分析[参见03H05, 28E05, 54J05]		Nonstandard analysis [See also 03H05, 28E05, 54J05]
26E40	构造性实分析[参见03F60]		Constructive real analysis [See also 03F60]
26E50	模糊实分析[参见03E72, 28E10]		Fuzzy real analysis [See also 03E72, 28E10]
26E60	平均[参见47A64]		Means [See also 47A64]
26E70	时间尺度或测度链上的实分析 (时间尺度或测度链上的动力学方程, 见34N05)		Real analysis on time scales or measure chains (For dynamic equations on time scales or measure chains see 34N05)
26E99	其它		None of the above, but in this section
28-XX	测度与积分(流形上的分析, 见58-XX)		Measure and integration (For analysis on manifolds, see 58-XX)
28-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
28-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
28-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
28-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
28-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
28-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
28Axx	经典测度论		Classical measure theory
28A05	集合类(Borel域、σ-环等), 可测集, Suslin集, 解析集[参见03E15, 26A21, 54H05]		Classes of sets (Borel fields, σ-rings, etc.), measurable sets, Suslin sets, analytic sets [See also 03E15, 26A21, 54H05]
28A10	实值或复值集合函数		Real- or complex-valued set functions
28A12	容度, 测度, 外测度, 容量		Contents, measures, outer measures, capacities
28A15	抽象微分理论, 集合函数的微分法[参见26A24]		Abstract differentiation theory, differentiation of set functions [See also 26A24]
28A20	可测函数与不可测函数, 可测函数序列, 收敛方式		Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
28A25	关于测度及其它集合函数的积分法		Integration with respect to measures and other set functions
28A33	测度空间, 测度的收敛性[参见46E27, 60Bxx]		Spaces of measures, convergence of measures [See also 46E27, 60Bxx]
28A35	积空间中的测度与积分		Measures and integrals in product spaces
28A50	测度的积分法与测度的蜕变		Integration and disintegration of measures
28A51	提升理论[参见46G15]		Lifting theory [See also 46G15]
28A60	Boole环上的测度, 测度代数[参见54H10]		Measures on Boolean rings, measure algebras [See also 54H10]
28A75	长度, 面积, 体积, 其它几何测度论[参见26B15, 49Q15]		Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
28A78	Hausdorff测度和填装测度		Hausdorff and packing measures
28A80	分形[参见37Fxx]		Fractals [See also 37Fxx]
28A99	其它		None of the above, but in this section
28Bxx	抽象空间中取值的集函数、测度与积分		Set functions, measures and integrals with values in abstract spaces
28B05	向量值集函数、测度与积分[参见46G10]		Vector-valued set functions, measures and integrals [See also 46G10]
28B10	群或半群值集函数、测度与积分		Group- or semigroup-valued set functions, measures and integrals
28B15	在有序空间中取值的集函数、测度与积分		Set functions, measures and integrals with values in ordered spaces
28B20	集值集函数与测度; 集值函数的积分法; 可测选择[参见26E25, 54C60, 54C65, 91B14]		Set-valued set functions and measures; integration of set-valued functions; measurable selections [See also 26E25, 54C60, 54C65, 91B14]
28B99	其它		None of the above, but in this section
28Cxx	附加结构空间上的集函数与测度[参见46G12, 58C35, 58D20]		Set functions and measures on spaces with additional structure [See also 46G12, 58C35, 58D20]
28C05	借助线性泛函的积分理论(Radon测度、Daniell积分等), 表示集函数与测度		Integration theory via linear functionals (Radon measures, Daniell integrals, etc.), representing set functions and measures
28C10	拓扑群或半群上的集函数与测度, Haar测度, 不变测度[参见22Axx, 43A05]		Set functions and measures on topological groups or semigroup, Haar measures, invariant measures [See also 22Axx, 43A05]
28C15	拓扑空间上的集函数与测度(测度的正则性等)		Set functions and measures on topological spaces (regularity of measures, etc.)
28C20	无限维空间中的集函数, 测度与积分(Wiener测度、Gauss测度等)[参见46G12, 58C35, 58D20, 60B11]		Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]
28C99	其它		None of the above, but in this section
28Dxx	测度论的遍历理论[参见11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]		Measure-theoretic ergodic theory [See also 11K50, 11K55, 22D40, 37Axx, 47A35, 54H20, 60Fxx, 60G10]
28D05	保测度变换		Measure-preserving transformations
28D10	保测度变换的单参数连续族		One-parameter continuous families of measure-preserving transformations
28D15	一般保测度变换群		General groups of measure-preserving transformations
28D20	熵和其它不变量		Entropy and other invariants
28D99	其它		None of the above, but in this section
28Exx	测度论中的杂题		Miscellaneous topics in measure theory
28E05	非标准测度论[参见03H05, 26E35]		Nonstandard measure theory [See also 03H05, 26E35]
28E10	模糊测度论[参见03E72, 26E50, 94D05]		Fuzzy measure theory [See also 03E72, 26E50, 94D05]
28E15	与逻辑及集合论的其它联系		Other connections with logic and set theory
28E99	其它		None of the above, but in this section
30-XX	单复变量函数(流形上的分析, 见58-XX)		Functions of a complex variable (For analysis on manifolds, see 58-XX)
30-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
30-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
30-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
30-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
30-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
30-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
30Axx	一般性质		General properties
30A05	复函数的单演性质(包括多因子单演函数和网状单演函数)		Monogenic properties of complex functions (including polygenic and areolar monogenic functions)
30A10	复域中的不等式		Inequalities in the complex domain
30A99	其它		None of the above, but in this section
30Bxx	级数展开		Series expansions
30B10	幂级数(包括缺项级数)		Power series (including lacunary series)
30B20	随机幂级数		Random power series
30B30	幂级数的边界特性, 超收敛性		Boundary behavior of power series, over-convergence
30B40	解析延拓		Analytic continuation
30B50	Dirichlet级数与其它级数展开, 指数级数[参见11M41, 42-XX]		Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
30B60	完备性问题, 函数系统的闭包		Completeness problems, closure of a system of functions
30B70	连分式[参见11A55, 40A15]		Continued fractions [See also 11A55, 40A15]
30B99	其它		None of the above, but in this section
30Cxx	几何函数论		Geometric function theory
30C10	多项式		Polynomials
30C15	多项式、有理函数及其它解析函数的零点(例如: 具有有界Dirichlet积分的函数的零点)(代数理论, 见12D10; 实方法, 见26C10)		Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) (For algebraic theory, see 12D10; for real methods, see 26C10)
30C20	特殊域的共形映射		Conformal mappings of special domains
30C25	共形映射理论中的覆盖定理		Covering theorems in conformal mapping theory
30C30	共形映射理论中的数值方法[参见65E05]		Numerical methods in conformal mapping theory [See also 65E05]
30C35	共形映射的一般理论		General theory of conformal mappings
30C40	核函数及其应用		Kernel functions and applications
30C45	特殊单叶和多叶函数类(星形的、凸的、有界旋度等)		Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
30C50	单叶和多叶函数的系数问题		Coefficient problems for univalent and multivalent functions
30C55	单叶和多叶函数的一般理论		General theory of univalent and multivalent functions
30C62	平面中的拟共形映射		Quasiconformal mappings in the plane
30C65	Rⁿ中的拟共形映射, 其它推广		Quasiconformal mappings in Rⁿ, other generalizations
30C70	共形和拟共形映射的极值问题, 变分法		Extremal problems for conformal and quasiconformal mappings, variational methods
30C75	共形和拟共形映射的极值问题, 其它方法		Extremal problems for conformal and quasiconformal mappings, other methods
30C80	极大值原理; Schwarz引理, Lindelöf原理, 模拟和推广; 从属运算		Maximum principle; Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C85	复平面中的容量与调和测度[参见31A15]		Capacity and harmonic measure in the complex plane [See also 31A15]
30C99	其它		None of the above, but in this section
30Dxx	整函数与亚纯函数, 及相关论题		Entire and meromorphic functions, and related topics
30D05	复域中的泛函方程, 解析函数的迭代与合成[参见34Mxx, 37Fxx, 39-XX]		Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]
30D10	整函数的级数与积分表示		Representations of entire functions by series and integrals
30D15	特殊整函数类及其增长估计		Special classes of entire functions and growth estimates
30D20	整函数, 一般理论		Entire functions, general theory
30D30	亚纯函数, 一般理论		Meromorphic functions, general theory
30D35	值分布, Nevanlinna理论		Distribution of values, Nevanlinna theory
30D40	聚类集合, 素端, 边界特性		Cluster sets, prime ends, boundary behavior
30D45	Bloch函数, 正规函数, 正规族		Bloch functions, normal functions, normal families
30D60	拟解析函数与其它函数类		Quasi-analytic and other classes of functions
30D99	其它		None of the above, but in this section
30Exx	复域中分析的杂题		Miscellaneous topics of analysis in the complex domain
30E05	矩问题, 插值问题		Moment problems, interpolation problems
30E10	复域中的逼近		Approximation in the complex domain
30E15	复域中的渐近表示		Asymptotic representations in the complex domain
30E20	积分法, Cauchy型积分, 解析函数的积分表示[参见45Exx]		Integration, integrals of Cauchy type, integral representations of analytic functions [See also 45Exx]
30E25	边值问题[参见45Exx]		Boundary value problems [See also 45Exx]
30E99	其它		None of the above, but in this section
30Fxx	Riemann曲面		Riemann surfaces
30F10	紧Riemann曲面和单值化[参见14H15, 32G15]		Compact Riemann surfaces and uniformization [See also 14H15, 32G15]
30F15	Riemann曲面上的调和函数		Harmonic functions on Riemann surfaces
30F20	Riemann曲面上的分类理论		Classification theory of Riemann surfaces
30F25	理想边界理论		Ideal boundary theory
30F30	Riemann曲面上的微分		Differentials on Riemann surfaces
30F35	Fuchs群和自守函数[参见11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]		Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx]
30F40	Klein群[参见20H10]		Kleinian groups [See also 20H10]
30F45	共形度量(双曲的, Poncairé, 距离函数)		Conformal metrics (hyperbolic, Poincaré, distance functions)
30F50	Klein曲面		Klein surfaces
30F60	Teichmüller理论[参见32G15]		Teichmüller theory [See also 32G15]
30F99	其它		None of the above, but in this section
30Gxx	广义函数论		Generalized function theory
30G06	非Archimedes函数论[参见12J25]; 非标准函数论[参见03H05]		Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05]
30G12	细全纯函数与拓扑函数论		Finely holomorphic functions and topological function theory
30G20	Bers或Vekua型推广(伪解析的、p-解析的等)		Generalizations of Bers or Vekua type (pseudoanalytic, p-analytic, etc.)
30G25	离散解析函数		Discrete analytic functions
30G30	解析函数的其它推广(包括抽象值函数)		Other generalizations of analytic functions (including abstract-valued functions)
30G35	超复变量函数与广义变量函数		Functions of hypercomplex variables and generalized variables
30G99	其它		None of the above, but in this section
30Hxx	解析函数的空间和代数		Spaces and algebras of analytic functions
30H05	有界解析函数		Bounded analytic functions
30H10	Hardy空间		Hardy spaces
30H15	Nevanlinna类和 Smirnov类		Nevanlinna class and Smirnov class
30H20	Bergman空间, Fock空间		Bergman spaces, Fock spaces
30H25	Besov空间和Q_p-空间		Besov spaces and Q_p-spaces
30H30	Bloch空间		Bloch spaces
30H35	BMO-空间		BMO-spaces
30H50	解析函数的代数		Algebras of analytic functions
30H80	Corona理论		Corona theorems
30H99	其它		None of the above, but in this section
30Jxx	圆盘上的函数论		Function theory on the disc
30J05	内函数		Inner functions
30J10	Blaschke积		Blaschke products
30J15	奇异内函数		Singular inner functions
30J99	其它		None of the above, but in this section
30Kxx	通用全纯函数		Universal holomorphic functions
30K05	通用Taylor级数		Universal Taylor series
30K10	通用Dirichlet级数		Universal Dirichlet series
30K15	有界通用函数		Bounded universal functions
30K20	复合通用性		Compositional universality
30K99	其它		None of the above, but in this section
30Lxx	度量空间上的分析		Analysis on metric spaces
30L05	度量空间的几何嵌入		Geometric embeddings of metric spaces
30L10	度量空间的拟共形映射		Quasiconformal mappings in metric spaces
30L99	其它		None of the above, but in this section
31-XX	位势论(概率位势论, 见60J45)		Potential theory (For probabilistic potential theory, see 60J45)
31-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
31-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
31-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
31-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
31-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
31-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
31Axx	二维理论		Two-dimensional theory
31A05	调和、次调和、上调和函数		Harmonic, subharmonic, superharmonic functions
31A10	积分表示, 积分算子, 积分方程法		Integral representations, integral operators, integral equations methods
31A15	位势和容量, 调和测度, 极值长度[参见30C85]		Potentials and capacity, harmonic measure, extremal length [See also 30C85]
31A20	边界性态(Fatou型定理等)		Boundary behavior (theorems of Fatou type, etc.)
31A25	边值问题和逆问题		Boundary value and inverse problems
31A30	双调和、多调和函数与方程, Poisson方程		Biharmonic, polyharmonic functions and equations, Poisson’s equation
31A35	与微分方程的联系		Connections with differential equations
31A99	其它		None of the above, but in this section
31Bxx	高维理论		Higher-dimensional theory
31B05	调和、次调和、上调和函数		Harmonic, subharmonic, superharmonic functions
31B10	积分表示, 积分算子, 积分方程法		Integral representations, integral operators, integral equations methods
31B15	位势和容量, 极值长度		Potentials and capacities, extremal length
31B20	边值问题和逆问题		Boundary value and inverse problems
31B25	边界性态		Boundary behavior
31B30	双调和、多调和方程与函数		Biharmonic and polyharmonic equations and functions
31B35	与微分方程的联系		Connections with differential equations
31B99	其它		None of the above, but in this section
31Cxx	其它推广		Other generalizations
31C05	调和、次调和、上调和函数		Harmonic, subharmonic, superharmonic functions
31C10	多重调和与多重次调和函数[参见32U05]		Pluriharmonic and plurisubharmonic functions [See also 32U05]
31C12	Riemann流形上位势论[参见53C20; Hodge理论, 见58A14]		Potential theory on Riemannian manifolds [See also 53C20; for Hodge theory, see 58A14]
31C15	位势和容量		Potentials and capacities
31C20	离散位势论和数值方法		Discrete potential theory and numerical methods
31C25	Dirichlet空间		Dirichlet spaces
31C35	Martin边界理论[参见60J50]		Martin boundary theory [See also 60J50]
31C40	细位势论		Fine potential theory
31C45	其它推广(非线性位势论等)		Other generalizations (nonlinear potential theory, etc.)
31C99	其它		None of the above, but in this section
31Dxx	公理位势论		Axiomatic potential theory
31D05	公理位势论		Axiomatic potential theory
31D99	其它		None of the above, but in this section
31Exx	度量空间的位势论		Potential theory on metric spaces
31E05	度量空间的位势论		Potential theory on metric spaces
31E99	其它		None of the above, but in this section
32-XX	多复变量与解析空间(无限维正则, 见46G20, 58B12)		Several complex variables and analytic spaces (For infinite-dimensional holomorphy, see 46G20, 58B12)
32-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
32-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
32-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
32-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
32-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
32-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
32Axx	多复变量全纯函数		Holomorphic functions of several complex variables
32A05	幂级数, 函数级数		Power series, series of functions
32A07	特殊域(Reinhardt, Hartogs, 圆, 管)		Special domains (Reinhardt, Hartogs, circular, tube)
32A10	全纯函数		Holomorphic functions
32A12	多值函数		Multifunctions
32A15	整函数		Entire functions
32A17	特殊函数族		Special families of functions
32A18	Bloch函数, 正规函数		Bloch functions, normal functions
32A19	函数的正规族, 映射		Normal families of functions, mappings
32A20	亚纯函数		Meromorphic functions
32A22	Nevanlinna理论(局部的); 增长估计; 其它不等式(几何理论, 见32H25, 32H30)		Nevanlinna theory (local); growth estimates; other inequalities (For geometric theory, see 32H25, 32H30)
32A25	积分表示; 标准核(Szegö、Bergman等)		Integral representations; canonical kernels (Szegö, Bergman, etc.)
32A26	积分表示, 构造核(例如: Cauchy, Fantappiè型核)		Integral representations, constructed kernels (e.g. Cauchy, Fantappiè-type kernels)
32A27	剩余的局部理论[参见32C30]		Local theory of residues [See also 32C30]
32A30	单复变量函数理论的其它推广(还必须在30-XX中至少指定一个分类号)(多超复变量函数, 见30G35)		Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) (For functions of several hypercomplex variables, see 30G35)
32A35	H^p空间, Nevanlinna空间[参见32M15, 42B30, 43A85, 46J15]		H^p-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
32A36	Bergman空间		Bergman spaces
32A37	全纯函数的其它空间(例如: 有界平均振荡(BMOA), 消没平均振荡(VMOA))[参见46Exx]		Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
32A38	全纯函数的代数[参见30H05, 46J10, 46J15]		Algebras of holomorphic functions [See also 30H05, 46J10, 46J15]
32A40	全纯函数的边界特性		Boundary behavior of holomorphic functions
32A45	超函数[参见46F15]		Hyperfunctions [See also 46F15]
32A50	多复变量的调和分析[主要见43-XX]		Harmonic analysis of several complex variables [See mainly 43-XX]
32A55	奇异积分		Singular integrals
32A60	全纯函数的零点集		Zero sets of holomorphic functions
32A65	Banach代数方法[主要见46Jxx]		Banach algebra techniques [See mainly 46Jxx]
32A70	泛函分析方法[主要见46Exx]		Functional analysis techniques [See mainly 46Exx]
32A99	其它		None of the above, but in this section
32Bxx	局部解析几何[参见13-XX, 14-XX]		Local analytic geometry [See also 13-XX and 14-XX]
32B05	解析代数及其推广, 预备定理		Analytic algebras and generalizations, preparation theorems
32B10	解析集的芽, 局部参数化		Germs of analytic sets, local parametrization
32B15	仿射空间的解析子集		Analytic subsets of affine space
32B20	半解析集与子解析集[参见14P15]		Semi-analytic sets and subanalytic sets [See also 14P15]
32B25	三角剖分与有关问题		Triangulation and related questions
32B99	其它		None of the above, but in this section
32Cxx	解析空间		Analytic spaces
32C05	实解析流形, 实解析空间[参见14Pxx, 58A07]		Real-analytic manifolds, real-analytic spaces [See also 14Pxx, 58A07]
32C07	实解析集, 复Nash函数[参见14P15, 14P20]		Real-analytic sets, complex Nash functions [See also 14P15, 14P20]
32C09	实解析流形的嵌入		Embedding of real analytic manifolds
32C11	复超几何[参见14A22, 14M30, 58A50]		Complex supergeometry [See also 14A22, 14M30, 58A50]
32C15	复空间		Complex spaces
32C18	解析空间的拓扑		Topology of analytic spaces
32C20	正规解析空间		Normal analytic spaces
32C22	解析空间的嵌入		Embedding of analytic spaces
32C25	解析子集与子流形		Analytic subsets and submanifolds
32C30	解析集和解析空间上的积分法, 流(局部理论, 见32A25或32A27)		Integration on analytic sets and spaces, currents (For local theory, see 32A25 or 32A27)
32C35	解析层和上同调群[参见14Fxx, 18F20, 55N30]		Analytic sheaves and cohomology groups [See also 14Fxx, 18F20, 55N30]
32C36	解析空间的局部上同调		Local cohomology of analytic spaces
32C37	对偶定理		Duality theorems
32C38	微分算子的层及其模, D-模[参见14F10, 16S32, 35A27, 58J15]		Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]
32C55	复空间中Levi问题; 推广		The Levi problem in complex spaces; generalizations
32C81	应用于物理		Applications to physics
32C99	其它		None of the above, but in this section
32Dxx	解析延拓		Analytic continuation
32D05	全纯域		Domains of holomorphy
32D10	全纯包络		Envelopes of holomorphy
32D15	解析目标的延拓		Continuation of analytic objects
32D20	可去奇点		Removable singularities
32D26	Riemann域		Riemann domains
32D99	其它		None of the above, but in this section
32Exx	全纯凸性		Holomorphic convexity
32E05	全纯凸复空间, 约化理论		Holomorphically convex complex spaces, reduction theory
32E10	Stein空间, Stein流形		Stein spaces, Stein manifolds
32E20	多项式凸性		Polynomial convexity
32E30	全纯与多项式逼近, Runge对, 插值(法)		Holomorphic and polynomial approximation, Runge pairs, interpolation
32E35	全纯函数的整体边界特性		Global boundary behavior of holomorphic functions
32E40	Levi问题		The Levi problem
32E99	其它		None of the above, but in this sect
32Fxx	几何凸性		Geometric convexity
32F10	q-凸性, q-凹性		q-convexity, q-concavity
32F17	其它凸性概念		Other notions of convexity
32F18	有限型条件		Finite-type conditions
32F27	几何凸性的拓扑推论		Topological consequences of geometric convexity
32F32	几何凸性的解析推论(消没定理等)		Analytical consequences of geometric convexity (vanishing theorems, etc.)
32F45	不变度量及其伪距离		Invariant metrics and pseudodistances
32F99	其它		None of the above, but in this section
32Gxx	解析结构的形变		Deformations of analytic structures
32G05	复结构的形变[参见13D10, 16S80, 58H10, 58H15]		Deformations of complex structures [See also 13D10, 16S80, 58H10, 58H15]
32G07	特殊(例如: CR)结构的形变		Deformations of special (e.g. CR) structures
32G08	纤维丛的形变		Deformations of fiber bundles
32G10	子流形与子空间的形变		Deformations of submanifolds and subspaces
32G13	解析模问题(代数模问题, 见14D20, 14D22, 14H10, 14J10)[参见14H15, 14J15]		Analytic moduli problems (For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10) [See also 14H15, 14J15]
32G15	Riemann曲面的模, Teichmüller理论[参见14H15, 30Fxx]		Moduli of Riemann surfaces, Teichmüller theory [See also 14H15, 30Fxx]
32G20	周期矩阵, Hodge结构的变分; 退化[参见14D05, 14D07, 14K30]		Period matrices, variation of Hodge structure; degenerations [See also 14D05, 14D07, 14K30]
32G34	常微分方程的模与形变(例如: Knizhnik-Zamolodchikov方程)[参见34Mxx]		Moduli and deformations for ordinary differential equations (e.g. Khnizhnik-Zamolodchikov equation) [See also 34Mxx]
32G81	应用于物理		Applications to physics
32G99	其它		None of the above, but in this section
32Hxx	全纯映射与对应		Holomorphic mappings and correspondences
32H02	全纯映射, (全纯)嵌入及其相关问题		Holomorphic mappings, (holomorphic) embeddings and related questions
32H04	亚纯映射		Meromorphic mappings
32H12	边界映射的唯一性		Boundary uniqueness of mappings
32H25	Picard型定理及其推广(函数理论性质, 见32A22)		Picard-type theorems and generalizations (For function-theoretic properties, see 32A22)
32H30	高维值分布理论(函数理论性质, 见32A22)		Value distribution theory in higher dimensions (For function-theoretic properties, see 32A22)
32H35	真映射, 有限性定理		Proper mappings, finiteness theorems
32H40	映射的边界正则性		Boundary regularity of mappings
32H50	迭代问题		Iteration problems
32H99	其它		None of the above, but in this section
32Jxx	紧解析空间(Riemann曲面, 见14Hxx, 30Fxx; 代数理论, 见14Jxx)		Compact analytic spaces (For Riemann surfaces, see 14Hxx, 30Fxx; for algebraic theory, see 14Jxx)
32J05	解析空间的紧化		Compactification of analytic spaces
32J10	代数相关定理		Algebraic dependence theorems
32J15	紧曲面		Compact surfaces
32J17	紧3重		Compact 3-folds
32J18	紧n重		Compact n-folds
32J25	代数几何的超越方法[参见14C30]		Transcendental methods of algebraic geometry [See also 14C30]
32J27	紧Kähler流形: 推广, 分类		Compact Kähler manifolds: generalizations, classification
32J81	应用于物理		Applications to physics
32J99	其它		None of the above, but in this section
32Kxx	解析空间的推广(还应在32-XX中至少指定一个分类号)		Generalizations of analytic spaces (should also be assigned at least one other classification number from Section 32 describing the type of problem)
32K05	Banach解析空间[参见58Bxx]		Banach analytic spaces [See also 58Bxx]
32K07	形式与分次复空间[参见58C50]		Formal and graded complex spaces [See also 58C50]
32K15	解析空间上的可微函数, 可微空间[参见58C25]		Differentiable functions on analytic spaces, differentiable spaces [See also 58C25]
32K99	其它		None of the above, but in this section
32Lxx	全纯纤维空间[参见55Rxx]		Holomorphic fiber spaces [See also 55Rxx]
32L05	全纯丛及其推广		Holomorphic bundles and generalizations
32L10	全纯向量丛的截面层与截面上同调, 一般结果[参见14F05, 18F20, 55N30]		Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30]
32L15	丛凸性[参见32F10]		Bundle convexity [See also 32F10]
32L20	消没定理		Vanishing theorems
32L25	扭子理论, 二重纤维化[参见53C28]		Twistor theory, double fibrations [See also 53C28]
32L81	应用于物理		Applications to physics
32L99	其它		None of the above, but in this section
32Mxx	有一个自同构群的复空间		Complex spaces with a group of automorphisms
32M05	复Lie群, 作用于复空间的自同构群[参见22E10]		Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
32M10	齐次复流形[参见14M17, 57T15]		Homogeneous complex manifolds [See also 14M17, 57T15]
32M12	殆齐次流形和空间[参见14M17]		Almost homogeneous manifolds and spaces [See also 14M17]
32M15	Hermite对称空间, 有界对称域, Jordan代数[参见22E10, 22E40, 53C35, 57T15]		Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras [See also 22E10, 22E40, 53C35, 57T15]
32M17	Cⁿ的自同构群和仿射流形		Automorphism groups of Cⁿ and affine manifolds
32M25	复向量场		Complex vector fields
32M99	其它		None of the above, but in this section
32Nxx	自守函数[参见11Fxx, 20H10, 22E40, 30F35]		Automorphic functions [See also 11Fxx, 20H10, 22E40, 30F35]
32N05	多复变量自守函数的一般理论		General theory of automorphic functions of several complex variables
32N10	自守型		Automorphic forms
32N15	对称域中的自守函数		Automorphic functions in symmetric domains
32N99	其它		None of the above, but in this section
32Pxx	非Archimedes分析(应在描述该问题的32-XX中至少指定一个其它分类号)		Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
32P05	非Archimedes分析(应在描述该问题的32-XX中至少指定一个其它分类号)		Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
32P99	其它		None of the above, but in this section
32Qxx	复流形		Complex manifolds
32Q05	负曲率流形		Negative curvature manifolds
32Q10	正曲率流形		Positive curvature manifolds
32Q15	Kähler流形		Kähler manifolds
32Q20	Kähler-Einstein流形[参见53Cxx]		Kähler-Einstein manifolds [See also 53Cxx]
32Q25	Calabi-Yau理论[参见14J32]		Calabi-Yau theory [See also 14J30]
32Q26	稳定性概念		Notions of stability
32Q28	Stein流形		Stein manifolds
32Q30	单值化		Uniformization
32Q35	作为Euclid空间子域的复流形		Complex manifolds as subdomains of Euclidean space
32Q40	嵌入定理		Embedding theorems
32Q45	双曲和Kobayashi双曲流形		Hyperbolic and Kobayashi hyperbolic manifolds
32Q55	复流形的拓扑方面		Topological aspects of complex manifolds
32Q57	分类定理		Classification theorems
32Q60	殆复流形		Almost complex manifolds
32Q65	伪全纯曲线		Pseudoholomorphic curves
32Q99	其它		None of the above, but in this section
32Sxx	奇异性[参见58Kxx]		Singularities [See also 58Kxx]
32S05	局部奇异性[参见14J17]		Local singularities [See also 14J17]
32S10	解析局部环的不变量		Invariants of analytic local rings
32S15	等奇异性(拓扑的与解析的)[参见14E15]		Equisingularity (topological and analytic) [See also 14E15]
32S20	奇异性的整体理论; 上同调性质[参见14E15]		Global theory of singularities; cohomological properties [See also 14E15]
32S22	与超平面排列的关系[参见52C35]		Relations with arrangements of hyperplanes [See also 52C35]
32S25	曲面和超曲面的奇异性[参见14J17]		Surface and hypersurface singularities [See also 14J17]
32S30	奇异性的形变; 消没周期[参见14B07]		Deformations of singularities; vanishing cycles [See also 14B07]
32S35	奇异簇的混合Hodge理论[参见14C30, 14D07]		Mixed Hodge theory of singular variety [See also 14C30, 14D07]
32S40	单值(性); 与微分方程及D-模的关系		Monodromy; relations with differential equations and D-modules
32S45	修正; 奇异性的分解[参见14E15]		Modifications; resolution of singularities [See also 14E15]
32S50	拓扑方面: Lefschetz定理, 拓扑分类, 不变量		Topological aspects: Lefschetz theorems, topological classification, invariants
32S55	Milnor纤维化; 与纽结理论的关系[参见57M25, 57Q45]		Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
32S60	分层; 可构成层; 相交上同调[参见58Kxx]		Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]
32S65	全纯向量场和叶状结构的奇异性		Singularities of holomorphic vector fields and foliations
32S70	奇异性的其它运算		Other operations on singularities
32S99	其它		None of the above, but in this section
32Txx	伪凸域		Pseudoconvex domains
32T05	正则域		Domains of holomorphy
32T15	强伪凸域		Strongly pseudoconvex domains
32T20	Worm域		Worm domains
32T25	有限型域		Finite type domains
32T27	弱伪凸边界上几何及其解析不变量		Geometric and analytic invariants on weakly pseudoconvex boundaries
32T35	穷举函数		Exhaustion functions
32T40	峰函数		Peak functions
32T99	其它		None of the above, but in this section
32Uxx	多重位势论		Pluripotential theory
32U05	多重次调和函数及推广[参见31C10]		Plurisubharmonic functions and generalizations [See also 31C10]
32U10	多重次调和穷举函数		Plurisubharmonic exhaustion functions
32U15	一般多重位势论		General pluripotential theory
32U20	容量理论及其推广		Capacity theory and generalizations
32U25	Lelong数		Lelong numbers
32U30	可去集		Removable sets
32U35	多重复Green函数		Pluricomplex Green functions
32U40	流动		Currents
32U99	其它		None of the above, but in this section
32Vxx	CR流形		CR manifolds
32V05	CR结构, CR算子, 及其推广		CR structures, CR operators, and generalizations
32V10	CR函数		CR functions
32V15	作为域边界的CR流形		CR manifolds as boundaries of domains
32V20	CR流形上的分析		Analysis on CR manifolds
32V25	函数的扩张及CR流形的其它解析对象		Extension of functions and other analytic objects from CR manifolds
32V30	CR流形的嵌入		Embeddings of CR manifolds
32V35	CR流形上的有限型条件		Finite type conditions on CR manifolds
32V40	复流形中的实子流形		Real submanifolds in complex manifolds
32V99	其它		None of the above, but in this section
32Wxx	多复变量微分算子		Differential operators in several complex variables
32W05	和-Neumann算子		and -Neumann operators
32W10	_b和_b-Neumann算子		_b and _b-Neumann operators
32W20	复Monge-Ampère算子		Complex Monge-Ampère operators
32W25	多复变量中的伪微分算子		Pseudodifferential operators in several complex variables
32W30	多复变量中的热核		Heat kernels in several complex variables
32W50	复分析的其它偏微分方程		Other partial differential equations of complex analysis
32W99	其它		None of the above, but in this section
33-XX	特殊函数(33-XX研究函数的性质)(正交函数, 见42Cxx; 组合方面, 见05Axx; 数论方面, 见11-XX; 表示理论, 见22Exx)		Special functions (33-XX deals with the properties of functions as functions) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx)
33-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
33-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
33-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
33-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
33-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
33-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
33Bxx	初等经典函数		Elementary classical functions
33B10	指数函数与三角函数		Exponential and trigonometric functions
33B15	Γ函数, β函数与多Γ函数		Gamma, beta and polygamma functions
33B20	不完全的β函数与Γ函数(误差函数, 概率积分, Fresnel积分)		Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals)
33B30	高阶对数函数		Higher logarithm functions
33B99	其它		None of the above, but in this section
33Cxx	超几何函数		Hypergeometric functions
33C05	经典超几何函数, ₂F₁		Classical hypergeometric functions, ₂F₁
33C10	Bessel函数与Airy函数, 柱函数, ₀F₁		Bessel and Airy functions, cylinder functions, ₀F₁
33C15	合流超几何函数, Whittaker函数, ₁F₁		Confluent hypergeometric functions, Whittaker functions, ₁F₁
33C20	广义超几何级数, _pF_q		Generalized hypergeometric series, _pF_q
33C45	超几何型的正交多项式和函数(Jacobi、Laguerre、Hermite、Askey格式等)[一般正交多项式和函数, 参见42C05]		Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]
33C47	其它特殊正交多项式和函数		Other special orthogonal polynomials and functions
33C50	可用单变量特殊函数表达的多变量正交多项式和函数		Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
33C52	与根系相关的正交多项式和函数		Orthogonal polynomials and functions associated with root systems
33C55	球面调和函数		Spherical harmonics
33C60	由其(E, G, H和I函数)定义的超几何积分和函数		Hypergeometric integrals and functions defined by them (E, G, H and I functions)
33C65	Appell, Horn和Lauricella函数		Appell, Horn and Lauricella functions
33C67	与根系相关的超几何函数		Hypergeometric functions associated with root systems
33C70	多变量中的其它超几何函数和积分		Other hypergeometric functions and integrals in several variables
33C75	作为超几何函数的椭圆积分		Elliptic integrals as hypergeometric functions
33C80	与群和代数的关系, 及其有关课题		Connections with groups and algebras, and related topics
33C90	应用		Applications
33C99	其它		None of the above, but in this section
33Dxx	基本超几何函数		Basic hypergeometric functions
33D05	q-Γ函数, q-β函数与积分		q-gamma functions, q-beta functions and integrals
33D15	单变量中的基本超几何函数, _rφ_s		Basic hypergeometric functions in one variable, _rφ_s
33D45	基本正交多项式和函数(Askey-Wilson多项式等)		Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33D50	可用单变量基本超几何函数表达的多变量正交多项式和函数		Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable
33D52	与根系相关的基本正交多项式和函数(Macdonald多项式等)		Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.)
33D60	基本超几何积分和由其定义的函数		Basic hypergeometric integrals and functions defined by them
33D65	双基本函数和多重基		Bibasic functions and multiple bases
33D67	与根系相关的基本超几何函数		Basic hypergeometric functions associated with root systems
33D70	多变量中的其它基本超几何函数和积分		Other basic hypergeometric functions and integrals in several variables
33D80	与量子群、Chevalley群、p-进群、Hecke代数及其相关课题的联系		Connections with quantum groups, Chevalley groups, p-adic groups, Hecke algebras, and related topics
33D90	应用		Applications
33D99	其它		None of the above, but in this section
33Exx	其它特殊函数		Other special functions
33E05	椭圆函数与积分		Elliptic functions and integrals
33E10	Lamé, Mathieu与球面波函数		Lamé, Mathieu, and spheroidal wave functions
33E12	Mittag-Leffer函数及其推广		Mittag-Leffler functions and generalizations
33E15	其它波函数		Other wave functions
33E17	Painlevé型函数		Painlevé-type functions
33E20	由级数和积分定义的其它函数		Other functions defined by series and integrals
33E30	来自微分、差分与积分方程的其它函数		Other functions coming from differential, difference and integral equations
33E50	特征p中的特殊函数(Γ函数等)		Special functions in characteristic p (gamma functions, etc.)
33E99	其它		None of the above, but in this section
33Fxx	计算方面		Computational aspects
33F05	数值逼近和赋值[参见65D20]		Numerical approximation and evaluation [See also 65D20]
33F10	符号计算(Gosper和Zeilberger算法等)[参见68W30]		Symbolic computation (Gosper and Zeilberger algorithms, etc.) [See also 68W30]
33F99	其它		None of the above, but in this section
34-XX	常微分方程		Ordinary differential equations
34-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
34-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
34-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
34-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
34-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
34-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
34Axx	一般理论		General theory
34A05	显式解和简化		Explicit solutions and reductions
34A07	模糊微分方程		Fuzzy differential equations
34A08	分式微分方程		Fractional differential equations
34A09	隐式方程, 微分-代数方程[参见65L80]		Implicit equations, differential-algebraic equations [See also 65L80]
34A12	解的初值问题、存在性、唯一性、连续依赖性及延拓		Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
34A25	解析理论: 级数、变换、变换式、运算微积分等[参见44-XX]		Analytical theory: series, transformations, transforms, operational calculus, etc. [See also 44-XX]
34A26	微分方程中的几何方法		Geometric methods in differential equations
34A30	线性方程与方程组, 一般理论		Linear equations and systems, general
34A33	格微分方程		Lattice differential equations
34A34	非线性方程与方程组, 一般理论		Nonlinear equations and systems, general
34A35	无限阶微分方程		Differential equations of infinite order
34A36	不连续方程		Discontinuous equations
34A37	带有脉冲的微分方程		Differential equations with impulses
34A38	混合系统		Hybrid systems
34A40	微分不等式[参见26D20]		Differential inequalities [See also 26D20]
34A45	解的理论逼近(数值分析, 见65Lxx)		Theoretical approximation of solutions (For numerical analysis, see 65Lxx)
34A55	逆问题		Inverse problems
34A60	微分包含[参见49J21, 49K21]		Differential inclusions [See also 49J21, 49K21]
34A99	其它		None of the above, but in this section
34Bxx	边值问题(常微分算子, 见34Lxx)		Boundary value problems (For ordinary differential operators, see 34Lxx)
34B05	线性边值问题		Linear boundary value problems
34B07	具有非线性依赖谱参数的线性边值问题		Linear boundary value problems with nonlinear dependence on the spectral parameter
34B08	参数依赖的边值问题		Parameter dependent boundary value problems
34B09	边界特征值问题		Boundary eigenvalue problems
34B10	非局部和多点边值问题		Nonlocal and multipoint boundary value problems
34B15	非线性边值问题		Nonlinear boundary value problems
34B16	奇异非线性边值问题		Singular nonlinear boundary value problems
34B18	非线性边值问题的正解		Positive solutions of nonlinear boundary value problems
34B20	Weyl理论及其推广		Weyl theory and its generalizations
34B24	Sturm-Liouville理论[参见34Lxx]		Sturm-Liouville theory [See also 34Lxx]
34B27	Green函数		Green functions
34B30	特殊方程(Mathieu、Hill、Bessel等)		Special equations (Mathieu, Hill, Bessel, etc.)
34B37	带有脉冲的边值问题		Boundary value problems with impulses
34B40	无穷区间上的边值问题		Boundary value problems on infinite intervals
34B45	图和网络上的边值问题		Boundary value problems on graphs and networks
34B60	应用		Applications
34B99	其它		None of the above, but in this section
34Cxx	定性理论[参见37-XX]		Qualitative theory [See also 37-XX]
34C05	积分曲线的位置, 奇异点, 极限环		Location of integral curves, singular points, limit cycles
34C07	多项式和解析向量场的极限环理论(存在性, 唯一性, 边界, Hilbert第16问题和分歧)		Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications)
34C08	与实代数几何的联系(fewnomials、非奇异化、Abel积分零点等)		Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)
34C10	振荡理论, 零点, 不共轭性和比较理论		Oscillation theory, zeros, disconjugacy and comparison theory
34C11	增长性、有界性		Growth, boundedness
34C12	单调系统		Monotone systems
34C14	对称性, 不变量		Symmetries, invariants
34C15	非线性振荡, 耦合振子		Nonlinear oscillations, coupled oscillators
34C20	方程和方程组的变换和约化, 正规型		Transformation and reduction of equations and systems, normal forms
34C23	分歧[主要见37Gxx]		Bifurcation [See mainly 37Gxx]
34C25	周期解		Periodic solutions
34C26	松弛振荡		Relaxation oscillations
34C27	殆周期解和伪殆周期解		Almost and pseudoalmost periodic solutions
34C28	复性态, 混沌系统[参见37Dxx]		Complex behavior, chaotic systems [See also 37Dxx]
34C29	平均方法		Averaging method
34C37	同宿解和异宿解		Homoclinic and heteroclinic solutions
34C40	流形上的方程及系统		Equations and systems on manifolds
34C41	等价性, 渐近等价		Equivalence, asymptotic equivalence
34C45	不变流形		Invariant manifolds
34C46	多频系统		Multifrequency systems
34C55	滞后		Hysteresis
34C60	定性研究和模型仿真		Qualitative investigation and simulation of models
34C99	其它		None of the above, but in this section
34Dxx	稳定性理论[参见37C75, 93Dxx]		Stability theory [See also 37C75, 93Dxx]
34D05	渐近性质		Asymptotic properties
34D06	同步		Synchronization
34D08	特征和Liapunov指数		Characteristic and Lyapunov exponents
34D09	二分法, 三分法		Dichotomy, trichotomy
34D10	摄动		Perturbations
34D15	奇摄动		Singular perturbations
34D20	稳定性		Stability
34D23	全局稳定性		Global stability
34D30	结构稳定性与模拟概念[参见37C20]		Structural stability and analogous concepts [See also 37C20]
34D35	解流形的稳定性		Stability of manifolds of solutions
34D45	吸引子[参见37C30, 37D45]		Attractors [See also 37C70, 37D45]
34D99	其它		None of the above, but in this section
34Exx	渐近理论		Asymptotic theory
34E05	渐近展开		Asymptotic expansions
34E10	摄动, 渐近		Perturbations, asymptotics
34E13	多重尺度法		Multiple scale methods
34E15	奇摄动, 一般理论		Singular perturbations, general theory
34E17	鸭解		Canard solutions
34E18	非标准分析法		Methods of nonstandard analysis
34E20	奇摄动, 转向点理论, WKB方法		Singular perturbations, turning point theory, WKB methods
34E99	其它		None of the above, but in this section
34Fxx	随机性的方程与方程组[参见34K50, 60H10, 93E03]		Equations and systems with randomness [See also 34K50, 60H10, 93E03]
34F05	随机性的方程与方程组[参见34K50, 60H10, 93E03]		Equations and systems with randomness [See also 34K50, 60H10, 93E03]
34F10	分歧		Bifurcation
34F15	共振现象		Resonance phenomena
34F99	其它		None of the above, but in this section
34Gxx	抽象空间中的微分方程[参见34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]		Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25]
34G10	线性方程[参见47D06, 47D09]		Linear equations [See also 47D06, 47D09]
34G20	非线性方程[参见47Hxx, 47Jxx]		Nonlinear equations [See also 47Hxx, 47Jxx]
34G25	发展包含		Evolution inclusions
34G99	其它		None of the above, but in this section
34Hxx	控制问题[参见49J15, 49K15, 93C15]		Control problems [See also 49J15, 49K15, 93C15]
34H05	控制问题[参见49J15, 49K15, 93C15]		Control problems [See also 49J15, 49K15, 93C15]
34H10	混沌控制		Chaos control
34H15	稳定化		Stabilization
34H20	分歧控制		Bifurcation control
34H99	其它		None of the above, but in this section
34Kxx	泛函-微分与微分-差分方程[参见37-XX]		Functional-differential and differential-difference equations [See also 37-XX]
34K05	一般理论		General theory
34K06	线性泛函-微分方程		Linear functional-differential equations
34K07	解的理论逼近		Theoretical approximation of solutions
34K08	泛函微分算子的谱理论		Spectral theory of functional-differential operators
34K09	泛函微分包含		Functional-differential inclusions
34K10	边值问题		Boundary value problems
34K11	振荡理论		Oscillation theory
34K12	解的增长性, 有界性, 比较		Growth, boundedness, comparison of solutions
34K13	周期解		Periodic solutions
34K14	殆周期解及伪周期解		Almost and pseudoperiodic solutions
34K17	方程和方程组的变换和简化, 标准型		Transformation and reduction of equations and systems, normal forms
34K18	分歧理论		Bifurcation theory
34K19	不变流形		Invariant manifolds
34K20	稳定性理论		Stability theory
34K21	稳态解		Stationary solutions
34K23	解的复(混沌)特性		Complex (chaotic) behavior of solutions
34K25	渐近理论		Asymptotic theory
34K26	奇摄动		Singular perturbations
34K27	摄动		Perturbations
34K28	解的数值逼近		Numerical approximation of solutions
34K29	逆问题		Inverse problems
34K30	抽象空间中的方程[参见34Gxx, 35R09, 35R10, 47Jxx]		Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx]
34K31	格泛函微分方程		Lattice functional-differential equations
34K32	隐式方程		Implicit equations
34K33	平均		Averaging
34K34	混合系统		Hybrid systems
34K35	控制问题[参见49J21, 49K21, 93C23]		Control problems [See also 49J21, 49K21, 93C23]
34K36	模糊泛函微分方程		Fuzzy functional-differential equations
34K37	具有分数导数的泛函微分方程		Functional-differential equations with fractional derivatives
34K38	泛函微分不等式		Functional-differential inequalities
34K40	中立型方程		Neutral equations
34K45	具有脉冲的方程		Equations with impulses
34K50	随机泛函-微分方程[参见60Hxx]		Stochastic functional-differential equations [See also 60Hxx]
34K60	定性分析和模型仿真		Qualitative investigation and simulation of models
34K99	其它		None of the above, but in this section
34Lxx	常微分算子[参见47E05]		Ordinary differential operators [See also 47E05]
34L05	一般谱论		General spectral theory
34L10	特征函数, 特征函数展开, 特征函数的完备性		Eigenfunction, eigenfunction expansions, completeness of eigenfunctions
34L15	特征值, 特征值的估计, 上界与下界		Eigenvalues, estimation of eigenvalues, upper and lower bounds
34L16	特征值与谱的其它部分的数值逼近		Numerical approximation of eigenvalues and of other parts of the spectrum
34L20	特征值的渐近分布, 特征函数的渐近理论		Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
34L25	散射理论, 逆散射		Scattering theory, inverse scattering
34L30	非线性常微分算子		Nonlinear ordinary differential operators
34L40	特殊算子(Dirac、一维Schrödinger等)		Particular operators (Dirac, one-dimensional Schrödinger, etc.)
34L99	其它		None of the above, but in this section
34Mxx	复域中的微分方程[参见30Dxx, 32G34]		Differential equations in the complex domain [See also 30Dxx, 32G34]
34M03	线性方程和方程组		Linear equations and systems
34M05	整解和亚纯解		Entire and meromorphic solutions
34M10	解的振荡和增长		Oscillation, growth of solutions
34M15	代数方面(微分-代数, 超超越性, 群理论)		Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical)
34M25	形式解, 变换技巧		Formal solutions, transform techniques
34M30	渐近性, 求和法		Asymptotics, summation methods
34M35	解的奇异性、单值[性]、局部性态, 标准型		Singularities, monodromy, local behavior of solutions, normal forms
34M40	Stokes现象和联络问题(线性和非线性)		Stokes phenomena and connection problems (linear and nonlinear)
34M45	复流形上的微分方程		Differential equations on complex manifolds
34M50	逆问题(Riemann-Hilbert、逆微分Galois等)		Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.)
34M55	Painlevé和其它特殊方程; 分类, 谱系		Painlevé and other special equations; classification, hierarchies
34M56	等单值形变		Isomonodromic deformations
34M60	复域中的奇摄动问题(复WKB, 转向点, 最速下降)[参见34E20]		Singular perturbation problems in the complex domain (complex WKB, turning points, steepest descent) [See also 34E20]
34M99	其它		None of the above, but in this section
34Nxx	时间尺度或测度链上的动力学方程(时间尺度上的实分析, 见26E70)		Dynamic equations on time scales or measure chains (For real analysis on time scales see 26E70)
34N05	时间尺度或测度链上的动力学方程 (时间尺度上的实分析, 见 26E70)		Dynamic equations on time scales or measure chains (For real analysis on time scales, see 26E70)
34N99	其它		None of the above, but in this section
35-XX	偏微分方程		Partial differential equations
35-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
35-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
35-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
35-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
35-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
35-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
35Axx	一般课题		General topics
35A01	存在性问题: 全局存在性, 局部存在性, 不存在性		Existence problems: global existence, local existence, nonexistence
35A02	唯一性问题: 全局唯一性, 局部唯一性, 不唯一性		Uniqueness problems: global uniqueness, local uniqueness, nonuniqueness
35A08	基本解		Fundamental solutions
35A09	经典解		Classical solutions
35A10	Cauchy-Kovalevskaya定理		Cauchy-Kovalevskaya theorems
35A15	变分法		Variational methods
35A16	拓扑和单调性方法		Topological and monotonicity methods
35A17	参数的		Parametrices
35A18	波前集		Wave front sets
35A20	解析方法, 奇异性		Analytic methods, singularities
35A21	奇异性的传播		Propagation of singularities
35A22	变换方法(例如: 积分变换)		Transform methods (e.g. integral transforms)
35A23	涉及导数、微分及积分算子的不等式, 积分不等式		Inequalities involving derivatives and differential and integral operators, inequalities for integrals
35A24	常微分方程的方法		Methods of ordinary differential equations
35A25	其它特殊方法		Other special methods
35A27	微局部方法; 偏微分方程中同调代数与层理论方法[参见32C38, 58J15]		Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]
35A30	几何理论, 特征, 变换[参见58J70, 58J72]		Geometric theory, characteristics, transformations [See also 58J70, 58J72]
35A35	解的理论逼近(数值分析, 见65Mxx, 65Nxx)		Theoretical approximation to solutions (For numerical analysis, see 65Mxx, 65Nxx)
35A99	其它		None of the above, but in this section
35Bxx	解的定性性质		Qualitative properties of solutions
35B05	振荡、解的零点、均值定理等		Oscillation, zeros of solutions, mean value theorems, etc.
35B06	对称、不变量等		Symmetries, invariants, etc.
35B07	轴对称解		Axially symmetric solutions
35B08	整解		Entire solutions
35B09	正解		Positive solutions
35B10	周期解		Periodic solutions
35B15	殆周期解及伪殆周期解		Almost and pseudo-almost periodic solutions
35B20	摄动		Perturbations
35B25	奇摄动		Singular perturbations
35B27	齐性化; 带有周期结构媒介中的方程[参见74Qxx, 76M50]		Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
35B30	依赖于初始和边界数据、参数的解[参见37Cxx]		Dependence of solutions on initial and boundary data, parameters [See also 37Cxx]
35B32	分歧[参见37Gxx, 37K50]		Bifurcation [See also 37Gxx, 37K50]
35B33	临界指数		Critical exponents
35B34	共振		Resonances
35B35	稳定性		Stability
35B36	模式形成		Pattern formation
35B38	临界点		Critical points
35B40	解的渐近特性		Asymptotic behavior of solutions
35B41	吸引子		Attractors
35B42	惯性流形		Inertial manifolds
35B44	爆破		Blow-up
35B45	先验估计		A priori estimates
35B50	极大值原理		Maximum principles
35B51	比较原理		Comparison principles
35B53	Liouville定理, Phragmén-Lindelöf定理		Liouville theorems, Phragmén-Lindelöf theorems
35B60	解的连续与延拓[参见58A15, 58A17, 58Hxx]		Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]
35B65	解的光滑性和正则性		Smoothness and regularity of solutions
35B99	其它		None of the above, but in this section
35Cxx	解的表示		Representations of solutions
35C05	闭型解		Solutions in closed form
35C06	自相似解		Self-similar solutions
35C07	行波解		Traveling wave solutions
35C08	孤子解		Soliton solutions
35C09	三角解		Trigonometric solutions
35C10	级数解		Series solutions
35C11	多项式解		Polynomial solutions
35C15	解的积分表示		Integral representations of solutions
35C20	渐近展开		Asymptotic expansions
35C99	其它		None of the above, but in this section
35Dxx	广义解		Generalized solutions
35D30	弱解		Weak solutions
35D35	强解		Strong solutions
35D40	粘性解		Viscosity solutions
35D99	其它		None of the above, but in this section
35Exx	带常系数的方程与方程组[参见35N05]		Equations and systems with constant coefficients [See also 35N05]
35E05	基本解		Fundamental solutions
35E10	凸性性质		Convexity properties
35E15	初值问题		Initial value problems
35E20	一般理论		General theory
35E99	其它		None of the above, but in this section
35Fxx	一般一阶方程与方程组		General first-order equations and systems
35F05	一阶线性方程		Linear first-order equations
35F10	一阶线性方程的初值问题		Initial value problems for linear first-order equations
35F15	一阶线性方程的边值问题		Boundary value problems for linear first-order equations
35F16	一阶线性方程的初-边值问题		Initial-boundary value problems for linear first-order equations
35F20	一阶非线性方程		Nonlinear first-order equations
35F21	Hamilton-Jacobi方程		Hamilton-Jacobi equations
35F25	一阶非线性方程的初值问题		Initial value problems for nonlinear first-order equations
35F30	一阶非线性方程的边值问题		Boundary value problems for nonlinear first-order equations
35F31	一阶非线性方程的初-边值问题		Initial-boundary value problems for nonlinear first-order equations
35F35	一阶线性方程组		Linear first-order systems
35F40	一阶线性方程组的初值问题		Initial value problems for linear first-order systems
35F45	一阶线性方程组的边值问题		Boundary value problems for linear first-order systems
35F46	一阶线性方程组的初-边值问题		Initial-boundary value problems for linear first-order systems
35F50	一阶非线性方程组		Nonlinear first-order systems
35F55	一阶非线性方程组的初值问题		Initial value problems for nonlinear first-order systems
35F60	一阶非线性方程组的边值问题		Boundary value problems for nonlinear first-order systems
35F61	一阶非线性方程组的初-边值问题		Initial-boundary value problems for nonlinear first-order systems
35F99	其它		None of the above, but in this section
35Gxx	一般高阶方程与方程组		General higher-order equations and systems
35G05	高阶线性方程		Linear higher-order equations
35G10	高阶线性方程的初值问题		Initial value problems for linear higher-order equations
35G15	高阶线性方程的边值问题		Boundary value problems for linear higher-order equations
35G16	高阶线性方程的初-边值问题		Initial-boundary value problems for linear higher-order equations
35G20	高阶非线性方程		Nonlinear higher-order equations
35G25	高阶非线性方程的初值问题		Initial value problems for nonlinear higher-order equations
35G30	高阶非线性方程的边值问题		Boundary value problems for nonlinear higher-order equations
35G31	高阶非线性方程的初-边值问题		Initial-boundary value problems for nonlinear higher-order equations
35G35	高阶线性方程组		Linear higher-order systems
35G40	高阶线性方程组的初值问题		Initial value problems for linear higher-order systems
35G45	高阶线性方程组的边值问题		Boundary value problems for linear higher-order systems
35G46	高阶线性方程组的初-边值问题		Initial-boundary value problems for linear higher-order systems
35G50	高阶非线性方程组		Nonlinear higher-order systems
35G55	高阶非线性方程组的初值问题		Initial value problems for nonlinear higher-order systems
35G60	高阶非线性方程组的边值问题		Boundary value problems for nonlinear higher-order systems
35G61	高阶非线性方程组的初-边值问题		Initial-boundary value problems for nonlinear higher-order systems
35G99	其它		None of the above, but in this section
35Hxx	封闭-椭圆型方程与方程组		Close-to-elliptic equations and systems
35H10	超椭圆型方程		Hypoelliptic equations
35H20	次椭圆型方程		Subelliptic equations
35H30	拟椭圆型方程		Quasi-elliptic equations
35H99	其它		None of the above, but in this section
35Jxx	椭圆型方程和方程组[参见58J10, 58J20]		Elliptic equations and systems [See also 58J10, 58J20]
35J05	Laplace方程, 约化波动方程(Helmholtz方程), Poisson方程[参见31Axx, 31Bxx]		Laplace equation, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx]
35J08	Green函数		Green’s functions
35J10	Schrödinger算子[参见35Pxx]		Schrödinger operator [See also 35Pxx]
35J15	二阶椭圆型方程		Second-order elliptic equations
35J20	二阶椭圆型方程的变分法		Variational methods for second-order elliptic equations
35J25	二阶椭圆型方程的边值问题		Boundary value problems for second-order elliptic equations
35J30	高阶椭圆型方程[参见31A30, 31B30]		Higher-order elliptic equations [See also 31A30, 31B30]
35J35	高阶椭圆型方程的变分法		Variational methods for higher-order elliptic equations
35J40	高阶椭圆型方程的边值问题		Boundary value problems for higher-order elliptic equations
35J46	一阶椭圆型方程组		First-order elliptic systems
35J47	二阶椭圆型方程组		Second-order elliptic systems
35J48	高阶椭圆型方程组		Higher-order elliptic systems
35J50	椭圆型方程组的变分法		Variational methods for elliptic systems
35J56	一阶椭圆型方程组的边值问题		Boundary value problems for first-order elliptic systems
35J57	二阶椭圆型方程组的边值问题		Boundary value problems for second-order elliptic systems
35J58	高阶椭圆型方程组的边值问题		Boundary value problems for higher-order elliptic systems
35J60	非线性椭圆型方程		Nonlinear elliptic equations
35J61	半线性椭圆型方程		Semilinear elliptic equations
35J62	拟线性椭圆型方程		Quasilinear elliptic equations
35J65	线性椭圆型方程的非线性边值问题		Nonlinear boundary value problems for linear elliptic equations
35J66	非线性椭圆型方程的非线性边值问题		Nonlinear boundary value problems for nonlinear elliptic equations
35J67	椭圆型方程解的边值问题		Boundary values of solutions to elliptic equations
35J70	退化椭圆型方程		Degenerate elliptic equations
35J75	奇异椭圆型方程		Singular elliptic equations
35J86	线性椭圆型单侧问题和线性椭圆型变分不等式[参见35R35, 49J40]		Linear elliptic unilateral problems and linear elliptic variational inequalities [See also 35R35, 49J40]
35J87	非线性椭圆型单侧问题和非线性椭圆型变分不等式[参见35R35, 49J40]		Nonlinear elliptic unilateral problems and nonlinear elliptic variational inequalities [See also 35R35, 49J40]
35J88	椭圆型变分不等式系统[参见35R35, 49J40]		Systems of elliptic variational inequalities [See also 35R35, 49J40]
35J91	具有Laplace, 双-Laplace或多-Laplace算子的半线性椭圆型方程		Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J92	具有p-Laplace算子的拟线性椭圆型方程		Quasilinear elliptic equations with p-Laplacian
35J93	具有平均曲率算子的拟线性椭圆型方程		Quasilinear elliptic equations with mean curvature operator
35J96	椭圆型Monge-Ampére方程		Elliptic Monge-Ampére equations
35J99	其它		None of the above, but in this section
35Kxx	抛物型方程与方程组[参见35Bxx, 35Dxx, 35R30, 35R35, 58J35]		Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]
35K05	热方程		Heat equation
35K08	热核		Heat kernel
35K10	二阶抛物型方程		Second-order parabolic equations
35K15	二阶抛物型方程的初值问题		Initial value problems for second-order parabolic equations
35K20	二阶抛物型方程的初-边值问题		Initial-boundary value problems for second-order parabolic equations
35K25	高阶抛物型方程		Higher-order parabolic equations
35K30	高阶抛物型方程的初值问题		Initial value problems for higher-order parabolic equations
35K35	高阶抛物型方程的初-边值问题		Initial-boundary value problems for higher-order parabolic equations
35K40	二阶抛物型方程组		Second-order parabolic systems
35K41	高阶抛物型方程组		Higher-order parabolic systems
35K45	二阶抛物型方程组的初值问题		Initial value problems for second-order parabolic systems
35K46	高阶抛物型方程组的初值问题		Initial value problems for higher-order parabolic systems
35K51	二阶抛物型方程组的初-边值问题		Initial-boundary value problems for second-order parabolic systems
35K52	高阶抛物型方程组的初-边值问题		Initial-boundary value problems for higher-order parabolic systems
35K55	非线性抛物型方程		Nonlinear parabolic equations
35K57	反应-扩散方程		Reaction-diffusion equations
35K58	半线性抛物型方程		Semilinear parabolic equations
35K59	拟线性抛物型方程		Quasilinear parabolic equations
35K60	线性抛物型方程的非线性初值问题		Nonlinear initial value problems for linear parabolic equations
35K61	非线性抛物型方程的非线性初-边值问题		Nonlinear initial-boundary value problems for nonlinear parabolic equations
35K65	退化抛物型方程		Degenerate parabolic equations
35K67	奇异抛物型方程		Singular parabolic equations
35K70	超抛物型方程、伪抛物型方程等		Ultraparabolic equations, pseudoparabolic equations, etc.
35K85	线性抛物型单侧问题和线性抛物型变分不等式[参见35R35, 49J40]		Linear parabolic unilateral problems and linear parabolic variational inequalities [See also 35R35, 49J40]
35K86	非线性抛物型单侧问题和非线性抛物型变分不等式[参见35R35, 49J40]		Nonlinear parabolic unilateral problems and nonlinear parabolic variational inequalities [See also 35R35, 49J40]
35K87	抛物型变分不等式系统[参见35R35, 49J40]		Systems of parabolic variational inequalities [See also 35R35, 49J40]
35K90	抽象抛物型方程		Abstract parabolic equations
35K91	具有Laplace、双-Laplace或多-Laplace算子的半线性抛物型方程		Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
35K92	具有p-Laplace算子的拟线性抛物型方程		Quasilinear parabolic equations with p-Laplacian
35K93	具有平均曲率算子的拟线性抛物型方程		Quasilinear parabolic equations with mean curvature operator
35K96	抛物型Monge-Ampére方程		Parabolic Monge-Ampére equations
35K99	其它		None of the above, but in this section
35Lxx	双曲型方程和方程组[参见58J45]		Hyperbolic equations and systems [See also 58J45]
35L02	一阶双曲型方程		First-order hyperbolic equations
35L03	一阶双曲型方程的初值问题		Initial value problems for first-order hyperbolic equations
35L04	一阶双曲型方程的初-边值问题		Initial-boundary value problems for first-order hyperbolic equations
35L05	波动方程		Wave equation
35L10	二阶双曲型方程		Second-order hyperbolic equations
35L15	二阶双曲型方程的初值问题		Initial value problems for second-order hyperbolic equations
35L20	二阶双曲型方程的初-边值问题		Initial-boundary value problems for second-order hyperbolic equations
35L25	高阶双曲型方程		Higher-order hyperbolic equations
35L30	高阶双曲型方程的初值问题		Initial value problems for higher-order hyperbolic equations
35L35	高阶双曲型方程的初-边值问题		Initial-boundary value problems for higher-order hyperbolic equations
35L40	一阶双曲型方程组		First-order hyperbolic systems
35L45	一阶双曲型方程组的初值问题		Initial value problems for first-order hyperbolic systems
35L50	一阶双曲型方程组的初-边值问题		Initial-boundary value problems for first-order hyperbolic systems
35L51	二阶双曲型方程组		Second-order hyperbolic systems
35L52	二阶双曲型方程组的初值问题		Initial value problems for second-order hyperbolic systems
35L53	二阶双曲型方程组的初-边值问题		Initial-boundary value problems for second-order hyperbolic systems
35L55	高阶双曲型方程组		Higher-order hyperbolic systems
35L56	高阶双曲型方程组的初值问题		Initial value problems for higher-order hyperbolic systems
35L57	高阶双曲型方程组的初-边值问题		Initial-boundary value problems for higher-order hyperbolic systems
35L60	一阶非线性双曲型方程		Nonlinear first-order hyperbolic equations
35L65	守恒律		Conservation laws
35L67	激波和奇异性[参见58Kxx, 76L05]		Shocks and singularities [See also 58Kxx, 76L05]
35L70	二阶非线性双曲型方程		Nonlinear second-order hyperbolic equations
35L71	二阶半线性双曲型方程		Semilinear second-order hyperbolic equations
35L72	二阶拟线性双曲型方程		Quasilinear second-order hyperbolic equations
35L75	高阶非线性双曲型方程		Nonlinear higher-order hyperbolic equations
35L76	高阶半线性双曲型方程		Semilinear higher-order hyperbolic equations
35L77	高阶拟线性双曲型方程		Quasilinear higher-order hyperbolic equations
35L80	退化双曲型方程		Degenerate hyperbolic equations
35L81	奇异双曲型方程		Singular hyperbolic equations
35L82	伪双曲型方程		Pseudohyperbolic equations
35L85	线性双曲型单侧问题和线性双曲型变分不等式[参见35R35, 49J40]		Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]
35L86	非线性双曲型单侧问题和非线性双曲型变分不等式[参见35R35, 49J40]		Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]
35L87	双曲型方程组的单侧问题和变分不等式[参见35R35, 49J40]		Unilateral problems and variational inequalities for hyperbolic systems [See also 35R35, 49J40]
35L90	抽象双曲型方程		Abstract hyperbolic equations
35L99	其它		None of the above, but in this section
35Mxx	特殊类型的方程和方程组(混合、复合等)		Equations and systems of special type (mixed, composite, etc.)
35M10	混合型方程		Equations of mixed type
35M11	混合型方程的初值问题		Initial value problems for equations of mixed type
35M12	混合型方程的边值问题		Boundary value problems for equations of mixed type
35M13	混合型方程的初-边值问题		Initial-boundary value problems for equations of mixed type
35M30	混合型方程组		Systems of mixed type
35M31	混合型方程组的初值问题		Initial value problems for systems of mixed type
35M32	混合型方程组的边值问题		Boundary value problems for systems of mixed type
35M33	混合型方程组的初-边值问题		Initial-boundary value problems for systems of mixed type
35M85	混合型线性单侧问题和变分不等式[参见35R35, 49J40]		Linear unilateral problems and variational inequalities of mixed type [See also 35R35, 49J40]
35M86	混合型非线性单侧问题和非线性变分不等式[参见35R35, 49J40]		Nonlinear unilateral problems and nonlinear variational inequalities of mixed type [See also 35R35, 49J40]
35M87	混合型变分不等式系统[参见35R35, 49J40]		Systems of variational inequalities of mixed type [See also 35R35, 49J40]
35M99	其它		None of the above, but in this section
35Nxx	超定组[参见58Hxx, 58J10, 58J15]		Overdetermined systems [See also 58Hxx, 58J10, 58J15]
35N05	常系数超定组		Overdetermined systems with constant coefficients
35N10	变系数超定组		Overdetermined systems with variable coefficients
35N15	-Neumann问题及推广; 形式复形[参见32W05, 32W10, 58J10]		-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]
35N20	超定初值问题		Overdetermined initial value problems
35N25	超定边值问题		Overdetermined boundary value problems
35N30	超定初-边值问题		Overdetermined initial-boundary value problems
35N99	其它		None of the above, but in this section
35Pxx	谱理论与特征值问题[参见47Axx, 47Bxx, 47F05]		Spectral theory and eigenvalue problems [See also 47Axx, 47Bxx, 47F05]
35P05	线性谱理论中的一般课题		General topics in linear spectral theory
35P10	特征函数的完备性, 特征函数展开		Completeness of eigenfunctions, eigenfunction expansions
35P15	特征值的估计, 上界与下界		Estimation of eigenvalues, upper and lower bounds
35P20	特征值与特征函数的渐近分布		Asymptotic distribution of eigenvalues and eigenfunctions
35P25	散射理论[参见47A40]		Scattering theory [See also 47A40]
35P30	非线性特征值问题, 非线性谱理论		Nonlinear eigenvalue problems, nonlinear spectral theory
35P99	其它		None of the above, but in this section
35Qxx	数理方程及在其它领域的应用[参见35J05, 35J10, 35K05, 35L05]		Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
35Q05	Euler-Poisson-Darboux方程		Euler-Poisson-Darboux equations
35Q15	Riemann-Hilbert问题[参见30E25, 31A25, 31B20]		Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
35Q20	Boltzmann方程		Boltzmann equations
35Q30	Navier-Stokes方程[参见76D05, 76D07, 76N10]		Navier-Stokes equations [See also 76D05, 76D07, 76N10]
35Q31	Euler方程[参见76D05, 76D07, 76N10]		Euler equations [See also 76D05, 76D07, 76N10]
35Q35	与流体力学有关的偏微分方程		PDEs in connection with fluid mechanics
35Q40	与量子力学有关的偏微分方程		PDEs in connection with quantum mechanics
35Q41	时间依赖的Schrödinger方程, Dirac方程		Time-dependent Schrödinger equations, Dirac equations
35Q51	类孤子方程[参见 37K40]		Soliton-like equations [See also 37K40]
35Q53	类KdV方程 (Korteweg-de Vries)[参见37K10]		KdV-like equations (Korteweg-de Vries) [See also 37K10]
35Q55	类NLS方程(非线性Schrödinger)[参见37K10]		NLS-like equations (nonlinear Schrödinger) [See also 37K10]
35Q56	Ginzburg-Landau方程		Ginzburg-Landau equations
35Q60	与光学和电磁理论有关的偏微分方程		PDEs in connection with optics and electromagnetic theory
35Q61	Maxwell方程		Maxwell equations
35Q62	与统计学有关的偏微分方程		PDEs in connection with statistics
35Q68	与计算机科学有关的偏微分方程		PDEs in connection with computer science
35Q70	与粒子及系统力学有关的偏微分方程		PDEs in connection with mechanics of particles and systems
35Q74	与变形固体力学有关的偏微分方程		PDEs in connection with mechanics of deformable solids
35Q75	与相对论和重力理论有关的偏微分方程		PDEs in connection with relativity and gravitational theory
35Q76	Einstein方程		Einstein equations
35Q80	与经典热力学及热传导有关的偏微分方程		PDEs in connection with classical thermodynamics and heat transfer
35Q82	与统计力学有关的偏微分方程		PDEs in connection with statistical mechanics
35Q83	类Vlasov方程		Vlasov-like equations
35Q84	Fokker-Planck方程		Fokker-Planck equations
35Q85	与天文学及天体物理学有关的偏微分方程		PDEs in connection with astronomy and astrophysics
35Q86	与地球物理学有关的偏微分方程		PDEs in connection with geophysics
35Q90	与数学规划有关的偏微分方程		PDEs in connection with mathematical programming
35Q91	与博弈论, 经济学, 社会学及行为科学有关的偏微分方程		PDEs in connection with game theory, economics, social and behavioral sciences
35Q92	与生物学及其它自然科学有关的偏微分方程		PDEs in connection with biology and other natural sciences
35Q93	与控制和最优化有关的偏微分方程		PDEs in connection with control and optimization
35Q94	与信息和通信有关的偏微分方程		PDEs in connection with information and communication
35Q99	其它		None of the above, but in this section
35Rxx	杂题(流形上的方程, 见58Jxx; 解的流形, 见58Bxx; 随机偏微分方程, 参见60H15)		Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see also 60H15)
35R01	流形上的偏微分方程[参见32Wxx, 53Cxx, 58Jxx]		Partial differential equations on manifolds [See also 32Wxx, 53Cxx, 58Jxx]
35R02	图和网络(分支或多边形空间)上的偏微分方程		Partial differential equations on graphs and networks (ramified or polygonal spaces)
35R03	Heisenberg群、Lie群、Carnot群等群上的偏微分方程		Partial differential equations on Heisenberg groups, Lie groups, Carnot groups, etc.
35R05	带有间断系数或数据的偏微分方程		Partial differential equations with discontinuous coefficients or data
35R06	带测度的偏微分方程		Partial differential equations with measure
35R09	积分-偏微分方程[参见45Kxx]		Integro-partial differential equations [See also 45Kxx]
35R10	偏泛函-微分方程		Partial functional-differential equations
35R11	分数偏微分方程		Fractional partial differential equations
35R12	脉冲偏微分方程		Impulsive partial differential equations
35R13	模糊偏微分方程		Fuzzy partial differential equations
35R15	无限维(例如: 函数)空间上的偏微分方程(=无穷多变量的偏微分方程)[参见46Gxx, 58D25]		Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25]
35R20	偏算子-微分方程(例如: 抽象空间赋值函数有限维空间的偏微分方程)[参见34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]		Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]
35R25	不适定问题		Improperly posed problems
35R30	逆问题		Inverse problems
35R35	自由边界问题		Free boundary problems
35R37	运动边界问题		Moving boundary problems
35R45	偏微分不等式		Partial differential inequalities
35R50	无限阶的偏微分方程		Partial differential equations of infinite order
35R60	具有随机性的偏微分方程, 随机偏微分方程[参见60H15]		Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]
35R70	多值右边的偏微分方程		Partial differential equations with multivalued right-hand sides
35R99	其它		None of the above, but in this section
35Sxx	伪微分算子与偏微分算子的其它推广[参见47G30, 58J40]		Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]
35S05	伪微分算子		Pseudodifferential operators
35S10	伪微分算子的初值问题		Initial value problems for pseudodifferential operators
35S11	伪微分算子的初-边值问题		Initial-boundary value problems for pseudodifferential operators
35S15	伪微分算子的边值问题		Boundary value problems for pseudodifferential operators
35S30	Fourier积分算子		Fourier integral operators
35S35	拓扑方面: 相交上同调、分层集等[参见32C38, 32S40, 32S60, 58J15]		Topological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]
35S50	仿微分算子		Paradifferential operators
35S99	其它		None of the above, but in this section
37-XX	动力系统和遍历理论[参见26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]		Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
37-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
37-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
37-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
37-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
37-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
37Axx	遍历理论[参见28Dxx]		Ergodic theory [See also 28Dxx]
37A05	保测变换		Measure-preserving transformations
37A10	保测变换的单参数连续族		One-parameter continuous families of measure-preserving transformations
37A15	保测变换的一般群[主要见22Fxx]		General groups of measure-preserving transformations [See mainly 22Fxx]
37A17	齐次流[参见22Fxx]		Homogeneous flows [See also 22Fxx]
37A20	轨道等价性, 余圈, 遍历等价关系		Orbit equivalence, cocycles, ergodic equivalence relations
37A25	遍历性, 混合, 混合速率		Ergodicity, mixing, rates of mixing
37A30	遍历定理, 谱论, Markov算子(算子遍历理论, 主要见47A35)		Ergodic theorems, spectral theory, Markov operators (For operator ergodic theory, see mainly 47A35)
37A35	熵和其它不变量, 同构, 分类		Entropy and other invariants, isomorphism, classification
37A40	非奇异(和无穷保测)变换		Nonsingular (and infinite-measure preserving) transformations
37A45	与数论和调和分析的关系[参见11Kxx]		Relations with number theory and harmonic analysis [See also 11Kxx]
37A50	与概率论和随机过程的关系[参见60Fxx和60G10]		Relations with probability theory and stochastic processes [See also 60Fxx and 60G10]
37A55	与C^*-代数理论的关系[主要见46L55]		Relations with the theory of C^*-algebras [See mainly 46L55]
37A60	统计力学中的动力系统[参见82Cxx]		Dynamical systems in statistical mechanics [See also 82Cxx]
37A99	其它		None of the above, but in this section
37Bxx	拓扑动力学[参见54H20]		Topological dynamics [See also 54H20]
37B05	具有特殊性质的变换和群作用(极小性、远离、邻近等)		Transformations and group actions with special properties (minimality, distality, proximality, etc.)
37B10	符号动力学[参见37Cxx, 37Dxx]		Symbolic dynamics [See also 37Cxx, 37Dxx]
37B15	细胞自动机[参见68Q80]		Cellular automata [See also 68Q80]
37B20	递归概念		Notions of recurrence
37B25	Lyapunov函数和稳定性; 吸引子, 排斥子		Lyapunov functions and stability; attractors, repellers
37B30	指标理论, Morse-Conley指标		Index theory, Morse-Conley indices
37B35	类梯度和递归性态; 孤立(局部-极大)不变集		Gradient-like and recurrent behavior; isolated (locally-maximal) invariant sets
37B40	拓扑熵		Topological entropy
37B45	动力学中的连续统理论		Continua theory in dynamics
37B50	有限型的多维移位, 贴砖动力学		Multi-dimensional shifts of finite type, tiling dynamics
37B55	非自治动力系统		Nonautonomous dynamical systems
37B99	其它		None of the above, but in this section
37Cxx	光滑动力系统: 一般理论[参见34Cxx, 34Dxx]		Smooth dynamical systems: general theory [See also 34Cxx, 34Dxx]
37C05	光滑映射和微分同胚		Smooth mappings and diffeomorphisms
37C10	向量场, 流, 常微分方程		Vector fields, flows, ordinary differential equations
37C15	拓扑与可微等价性, 共轭, 不变量, 模, 分类		Topological and differentiable equivalence, conjugacy, invariants, moduli, classification
37C20	一般性质, 结构稳定性		Generic properties, structural stability
37C25	不动点, 周期点, 不动点指数理论		Fixed points, periodic points, fixed-point index theory
37C27	向量场和流的周期轨道		Periodic orbits of vector fields and flows
37C29	同宿和异宿轨道		Homoclinic and heteroclinic orbits
37C30	ζ函数, (Ruelle-Frobenius)迁移算子, 动力系统中其它泛函分析方法		Zeta functions, (Ruelle-Frobenius) transfer operators, and other functional analytic techniques in dynamical systems
37C35	轨道增长性		Orbit growth
37C40	光滑遍历理论, 不变测度[参见37Dxx]		Smooth ergodic theory, invariant measures [See also 37Dxx]
37C45	动力系统的维数理论		Dimension theory of dynamical systems
37C50	近似轨道(伪轨道、影子等)		Approximate trajectories (pseudotrajectories, shadowing, etc.)
37C55	周期和拟周期流与微分同胚		Periodic and quasiperiodic flows and diffeomorphisms
37C60	非自治光滑动力系统[参见37B55]		Nonautonomous smooth dynamical systems [See also 37B55]
37C65	单调流		Monotone flows
37C70	吸引子和排斥子, 拓扑结构		Attractors and repellers, topological structure
37C75	稳定性理论		Stability theory
37C80	对称性等变动力系统		Symmetries, equivariant dynamical systems
37C85	群作用在除Z和R及叶状结构以外的动力学[主要见22Fxx, 也见57R30, 57Sxx]		Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
37C99	其它		None of the above, but in this section
37Dxx	具有双曲特性的动力系统		Dynamical systems with hyperbolic behavior
37D05	双曲轨道和集合		Hyperbolic orbits and sets
37D10	不变流形理论		Invariant manifold theory
37D15	Morse-Smale系统		Morse-Smale systems
37D20	一致双曲系统(扩张、Anosov、公理A等)		Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37D25	非一致双曲系统(Liapunov指数、Pesin理论等)		Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.)
37D30	部分双曲系统和受控分裂		Partially hyperbolic systems and dominated splittings
37D35	热力学形式体系, 变分原理, 平衡态		Thermodynamic formalism, variational principles, equilibrium states
37D40	几何原点的动力系统和双曲性(测地流和极限圆流等)		Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
37D45	奇怪吸引子, 混沌动力学		Strange attractors, chaotic dynamics
37D50	具有奇异性的双曲系统(台球等)		Hyperbolic systems with singularities (billiards, etc.)
37D99	其它		None of the above, but in this section
37Exx	低维动力系统		Low-dimensional dynamical systems
37E05	区间的映射(分段连续, 连续, 光滑)		Maps of the interval (piecewise continuous, continuous, smooth)
37E10	圆的映射		Maps of the circle
37E15	组合动力学(周期轨道型)		Combinatorial dynamics (types of periodic orbits)
37E20	通用性, 重正规化[参见37F25]		Universality, renormalization [See also 37F25]
37E25	树和图的映射		Maps of trees and graphs
37E30	平面和曲面的同胚和微分同胚		Homeomorphisms and diffeomorphisms of planes and surfaces
37E35	曲面上的流		Flows on surfaces
37E40	扭转映射		Twist maps
37E45	旋转数和向量		Rotation numbers and vectors
37E99	其它		None of the above, but in this section
37Fxx	复动力系统[参见30D05, 32H50]		Complex dynamical systems [See also 30D05, 32H50]
37F05	关系和对应		Relations and correspondences
37F10	多项式; 有理映射; 整函数和亚纯函数[参见32A10, 32A20, 32H02, 32H04]		Polynomials; rational maps; entire and meromorphic functions [See also 32A10, 32A20, 32H02, 32H04]
37F15	扩张映射; 双曲性; 结构稳定性		Expanding maps; hyperbolicity; structural stability
37F20	组合学和拓扑学		Combinatorics and topology
37F25	重正规化		Renormalization
37F30	拟共形方法和Teichmüller理论; 作为动力系统的Fuches和Klein群		Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems
37F35	共形密度和Hausdorff维数		Conformal densities and Hausdorff dimension
37F40	几何极限		Geometric limits
37F45	动力系统的全纯族; Mandelbrot集; 分歧		Holomorphic families of dynamical systems; the Mandelbrot set; bifurcations
37F50	小除子, 旋转域和线性化; Fatou和Julia集		Small divisors, rotation domains and linearization; Fatou and Julia sets
37F75	全纯叶状结构和向量场[参见32M25, 32S65, 34Mxx]		Holomorphic foliations and vector fields [See also 32M25, 32S65, 34Mxx]
37F99	其它		None of the above, but in this section
37Gxx	局部和非局部分歧理论[参见34C23, 34K18]		Local and nonlocal bifurcation theory [See also 34C23, 34K18]
37G05	标准型		Normal forms
37G10	奇异点的分歧		Bifurcations of singular points
37G15	极限环和周期轨道的分歧		Bifurcations of limit cycles and periodic orbits
37G20	具有同宿轨道的双曲奇异点		Hyperbolic singular points with homoclinic trajectories
37G25	分歧与非横截相交的关系		Bifurcations connected with nontransversal intersection
37G30	来自分歧的无限非游荡集		Infinite nonwandering sets arising in bifurcations
37G35	吸引子及其分歧		Attractors and their bifurcations
37G40	对称性等变分歧理论		Symmetries, equivariant bifurcation theory
37G99	其它		None of the above, but in this section
37Hxx	随机动力系统[参见15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]]		Random dynamical systems [See also 15B52, 34D08, 34F05, 47B80, 70L05, 82C05, 93Exx]
37H05	基础, 余圈的一般理论, 代数遍历理论[参见37Axx]		Foundations, general theory of cocycles, algebraic ergodic theory [See also 37Axx]
37H10	生成, 随机差分和微分方程[参见34F05, 34K50, 60H10, 60H15]		Generation, random and stochastic difference and differential equations [See also 34F05, 34K50, 60H10, 60H15]
37H15	乘性遍历理论, Lyapunov指数[参见34D08, 37Axx, 37Cxx, 37Dxx]		Multiplicative ergodic theory, Lyapunov exponents [See also 34D08, 37Axx, 37Cxx, 37Dxx]
37H20	分歧理论[参见37Gxx]		Bifurcation theory [See also 37Gxx]
37H99	其它		None of the above, but in this section
37Jxx	有限维Hamilton, Lagrange, 接触和非完整系统[参见53Dxx, 70Fxx, 70Hxx]		Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems [See also 53Dxx, 70Fxx, 70Hxx]
37J05	一般理论, 与辛几何和拓扑的关系		General theory, relations with symplectic geometry and topology
37J10	辛映射, 不动点		Symplectic mappings, fixed points
37J15	对称性, 不变量, 不变流形, 动量映射, 约化[参见53D20]		Symmetries, invariants, invariant manifolds, momentum maps, reduction [See also 53D20]
37J20	分歧问题		Bifurcation problems
37J25	稳定性问题		Stability problems
37J30	可积性阻碍(不可积性判据)		Obstructions to integrability (nonintegrability criteria)
37J35	完备可积系统, 相空间的拓扑结构, 积分法		Completely integrable systems, topological structure of phase space, integration methods
37J40	摄动, 标准型, 小除子, KAM理论, Arnol'd扩散		Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
37J45	周期的, 同宿和异宿轨道; 变分法, 度-理论方法		Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37J50	作用-极小化轨道和测度		Action-minimizing orbits and measures
37J55	接触系统[参见53D10]		Contact systems [See also 53D10]
37J60	非完整动力系统[参见70F25]		Nonholonomic dynamical systems [See also 70F25]
37J99	其它		None of the above, but in this section
37Kxx	无限维Hamilton系统[参见35Axx, 35Qxx]		Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]
37K05	Hamilton结构, 对称性, 变分原理, 守恒律		Hamiltonian structures, symmetries, variational principles, conservation laws
37K10	完备可积系统, 可积性检验, 双Hamilton结构, 谱系(KdV、KP、Toda等)		Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
37K15	逆谱和散射法的完备可积系统的积分法		Integration of completely integrable systems by inverse spectral and scattering methods
37K20	与代数几何、复分析、特殊函数的关系[参见14H70]		Relations with algebraic geometry, complex analysis, special functions [See also 14H70]
37K25	与微分几何的关系		Relations with differential geometry
37K30	与无限维Lie代数及其它代数结构的关系		Relations with infinite-dimensional Lie algebras and other algebraic structures
37K35	Lie-Bäcklund和其它变换		Lie-Bäcklund and other transformations
37K40	孤立子理论, 解的渐近特性		Soliton theory, asymptotic behavior of solutions
37K45	稳定性问题		Stability problems
37K50	分歧问题		Bifurcation problems
37K55	摄动, 无限维系统的KAM		Perturbations, KAM for infinite-dimensional systems
37K60	格动力学[参见37L60]		Lattice dynamics [See also 37L60]
37K65	微分同胚群上和映射与度量流形上的Hamilton系统		Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics
37K99	其它		None of the above, but in this section
37Lxx	无限维耗散动力系统[参见35Bxx, 35Qxx]		Infinite-dimensional dissipative dynamical systems [See also 35Bxx, 35Qxx]
37L05	一般理论, 非线性半群, 发展方程		General theory, nonlinear semigroups, evolution equations
37L10	标准型, 中心流形理论, 分歧理论		Normal forms, center manifold theory, bifurcation theory
37L15	稳定性问题		Stability problems
37L20	对称性		Symmetries
37L25	惯性流形和其它不变吸引集		Inertial manifolds and other invariant attracting sets
37L30	吸引子及其维数, Lyapunov指数		Attractors and their dimensions, Lyapunov exponents
37L40	不变测度		Invariant measures
37L45	双曲性; Lyapunov函数		Hyperbolicity; Lyapunov functions
37L50	非紧半群; 色散方程; Hamilton系统的摄动		Noncompact semigroups; dispersive equations; perturbations of Hamiltonian systems
37L55	无限维随机动力系统; 随机方程[参见35R60, 60H10, 60H15]		Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15]
37L60	格动力学[参见37K60]		Lattice dynamics [See also 37K60]
37L65	特殊近似法(非线性Galerkin等)		Special approximation methods (nonlinear Galerkin, etc.)
37L99	其它		None of the above, but in this section
37Mxx	近似法及动力系统的数值处理[参见65Pxx]		Approximation methods and numerical treatment of dynamical systems [See also 65Pxx]
37M05	仿真		Simulation
37M10	时间序列分析		Time series analysis
37M15	辛积分仪		Symplectic integrators
37M20	分歧问题的计算方法		Computational methods for bifurcation problems
37M25	遍历理论的计算方法(不变测度的逼近, Lyapunov指数的计算, 熵)		Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy)
37M99	其它		None of the above, but in this section
37Nxx	应用		Applications
37N05	经典和天体力学中的动力系统[主要见70Fxx, 70Hxx, 70Kxx]		Dynamical systems in classical and celestial mechanics [See mainly 70Fxx, 70Hxx, 70Kxx]
37N10	流体力学、海洋学和气象学中的动力系统[主要见76-XX, 特别地76D05, 76F20, 86A05, 86A10]		Dynamical systems in fluid mechanics, oceanography and meteorology [See mainly 76-XX, especially 76D05, 76F20, 86A05, 86A10]
37N15	固体力学中的动力系统[主要见74Hxx]		Dynamical systems in solid mechanics [See mainly 74Hxx]
37N20	物理学其它分支领域(量子力学, 一般相对论, 激光物理)中的动力系统		Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37N25	生物学中的动力系统[主要见92-XX, 也可见91-XX]		Dynamical systems in biology [See mainly 92-XX, but also 91-XX]
37N30	数值分析中的动力系统		Dynamical systems in numerical analysis
37N35	控制中的动力系统		Dynamical systems in control
37N40	最优化和经济学中的动力系统		Dynamical systems in optimization and economics
37N99	其它		None of the above, but in this section
37Pxx	算术和非Archimedes动力系统[参见11S82, 37A45]		Arithmetic and non-Archimedean dynamical systems [See also 11S82, 37A45]
37P05	多项式和有理映射		Polynomial and rational maps
37P10	解析和亚纯映射		Analytic and meromorphic maps
37P15	全局基域		Global ground fields
37P20	非Archimedes局部基域		Non-Archimedean local ground fields
37P25	有限基域		Finite ground fields
37P30	高度函数; Green函数;不变测度[参见11G50, 14G40]		Height functions; Green functions; invariant measures [See also 11G50, 14G40]
37P35	周期点的算术性质		Arithmetic properties of periodic points
37P40	非Archimedes Fatou及Julia集		Non-Archimedean Fatou and Julia sets
37P45	族和模空间		Families and moduli spaces
37P50	Berkovich空间的动力系统		Dynamical systems on Berkovich spaces
37P55	一般代数簇的算术动力学		Arithmetic dynamics on general algebraic varieties
37P99	其它		None of the above, but in this section
39-XX	差分方程与泛函方程		Difference and functional equations
39-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
39-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
39-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
39-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
39-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
39-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
39Axx	差分方程(动力系统, 见37-XX; 时间尺度上的动力学方程, 见34N05)		Difference equations (For dynamical systems, see 37-XX; for dynamic equations on time scales, see 34N05)
39A05	一般问题		General theory
39A06	线性方程		Linear equations
39A10	差分方程, 加性		Difference equations, additive
39A12	分析课题中的离散式		Discrete version of topics in analysis
39A13	差分方程, 尺度化(q-差分)[参见33Dxx]		Difference equations, scaling (q-differences) [See also 33Dxx]
39A14	偏差分方程		Partial difference equations
39A20	乘法和其它广义差分方程, 例如: Lyness型的		Multiplicative and other generalized difference equations, e.g. of Lyness type
39A21	振荡理论		Oscillation theory
39A22	解的增长性, 有界性及比较		Growth, boundedness, comparison of solutions
39A23	周期解		Periodic solutions
39A24	殆周期解		Almost periodic solutions
39A28	分歧理论		Bifurcation theory
39A30	稳定性理论		Stability theory
39A33	解的复(混沌)性态		Complex (chaotic) behavior of solutions
39A45	复域上的方程		Equations in the complex domain
39A50	随机差分方程		Stochastic difference equations
39A60	应用		Applications
39A70	差分算子[参见47B39]		Difference operators [See also 47B39]
39A99	其它		None of the above, but in this section
39Bxx	泛函方程和不等式[参见30D05]		Functional equations and inequalities [See also 30D05]
39B05	一般问题		General
39B12	迭代理论, 迭代和复合方程[参见26A18, 30D05, 37-XX]		Iteration theory, iterative and composite equations [See also 26A18, 30D05, 37-XX]
39B22	实函数方程[参见26A51, 26B25]		Equations for real functions [See also 26A51, 26B25]
39B32	复函数方程[参见30D05]		Equations for complex functions [See also 30D05]
39B42	矩阵与算子方程[参见47Jxx]		Matrix and operator equations [See also 47Jxx]
39B52	更一般域和/或范围上的函数方程		Equations for functions with more general domains and/or ranges
39B55	正交加性和其它条件方程		Orthogonal additivity and other conditional equations
39B62	泛函不等式, 包括次可加性、凸性等[参见26A51, 26B25, 26Dxx]		Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
39B72	泛函方程和不等式系统		Systems of functional equations and inequalities
39B82	稳定性, 分离, 扩张和相关课题[参见46A22]		Stability, separation, extension, and related topics [See also 46A22]
39B99	其它		None of the above, but in this section
40-XX	序列, 级数, 可(求)和性		Sequences, series, summability
40-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
40-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
40-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
40-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
40-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
40-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
40Axx	无穷极限过程的收敛与发散		Convergence and divergence of infinite limiting processes
40A05	级数与序列的收敛及发散		Convergence and divergence of series and sequences
40A10	积分的收敛与发散		Convergence and divergence of integrals
40A15	连分式的收敛与发散[参见30B70]		Convergence and divergence of continued fractions [See also 30B70]
40A20	无穷乘积的收敛与发散		Convergence and divergence of infinite products
40A25	极限值的逼近(级数求和等)(Euler-Maclaurin求和公式, 见65B15)		Approximation to limiting values (summation of series, etc.) (For the Euler-Maclaurin summation formula, see 65B15)
40A30	函数级数与序列的收敛及发散		Convergence and divergence of series and sequences of functions
40A35	理想和统计收敛[参见40G15]		Ideal and statistical convergence [See also 40G15]
40A99	其它		None of the above, but in this section
40Bxx	多重序列与级数		Multiple sequences and series
40B05	多重序列与级数(还应在这节中至少指定一个分类号)		Multiple sequences and series (should also be assigned at least one other classification number in this section)
40B99	其它		None of the above, but in this section
40Cxx	一般可(求)和性方法		General summability methods
40C05	矩阵法		Matrix methods
40C10	积分法		Integral methods
40C15	函数论方法(包括幂级数法和半连续法)		Function-theoretic methods (including power series methods and semicontinuous methods)
40C99	其它		None of the above, but in this section
40Dxx	可(求)和性的直接定理		Direct theorems on summability
40D05	一般定理		General theorems
40D09	可(求)和性域的结构		Structure of summability fields
40D10	Tauber常数和振荡极限		Tauberian constants and oscillation limits
40D15	收敛因子与可(求)和性因子		Convergence factors and summability factors
40D20	可(求)和性及方法的有界域		Summability and bounded fields of methods
40D25	包含和等价定理		Inclusion and equivalence theorems
40D99	其它		None of the above, but in this section
40Exx	反演定理		Inversion theorems
40E05	Tauber型定理, 一般理论		Tauberian theorems, general
40E10	增长估计		Growth estimates
40E15	缺项反演定理		Lacunary inversion theorems
40E20	Tauber常数		Tauberian constants
40E99	其它		None of the above, but in this section
40Fxx	绝对和强可(求)和性(还必须在40-XX中至少指定一个分类号)		Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
40F05	绝对和强可(求)和性(还必须在40-XX中至少指定一个分类号)		Absolute and strong summability (should also be assigned at least one other classification number in Section 40)
40F99	其它		None of the above, but in this section
40Gxx	可(求)和性的特殊方法		Special methods of summability
40G05	Cesàro, Euler, Nörlund和Hausdorff方法		Cesàro, Euler, Nörlund and Hausdorff methods
40G10	Abel, Borel与幂级数方法		Abel, Borel and power series methods
40G15	使用统计收敛的可(求)和性方法[参见40A35]		Summability methods using statistical convergence [See also 40A35]
40G99	其它		None of the above, but in this section
40Hxx	可(求)和性中的泛函分析法		Functional analytic methods in summability
40H05	可(求)和性中的泛函分析法		Functional analytic methods in summability
40H99	其它		None of the above, but in this section
40Jxx	抽象结构中的可(求)和性[参见43A55, 46A35, 46B15]		Summability in abstract structures [See also 43A55, 46A35, 46B15]
40J05	抽象结构中的可(求)和性[参见43A55, 46A35, 46B15](还必须在40-XX中至少指定一个分类号)		Summability in abstract structures [See also 43A55, 46A35, 46B15](should also be assigned at least one other classification number in this section)
40J99	其它		None of the above, but in this section
41-XX	逼近与展开(所有复域中的逼近论, 见30E05和30E10; 所有三角逼近与插值, 见42A10和42A15; 数值逼近, 见65Dxx)		Approximations and expansions (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx)
41-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
41-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
41-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
41-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
41-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
41-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
41Axx	逼近与展开(所有复域中的逼近论, 见30E05和30E10; 所有三角逼近与插值, 见42A10和42A15; 数值逼近, 见65Dxx)		Approximations and expansions (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx)
41A05	插值[参见42A15和65D05]		Interpolation [See also 42A15 and 65D05]
41A10	多项式逼近(三角多项式逼近, 见42A10)		Approximation by polynomials (For approximation by trigonometric polynomials, see 42A10)
41A15	样条逼近		Spline approximation
41A17	逼近不等式(Bernstein, Jackson, Nikol'skiǐ型不等式)		Inequalities in approximation (Bernstein, Jackson, Nikol'skiǐ-type inequalities)
41A20	有理函数逼近		Approximation by rational functions
41A21	Padé逼近		Padé approximation
41A25	收敛速率, 逼近度		Rate of convergence, degree of approximation
41A27	逆定理		Inverse theorems
41A28	同时逼近		Simultaneous approximation
41A29	带约束逼近		Approximation with constraints
41A30	其它特殊函数类的逼近		Approximation by other special function classes
41A35	算子逼近(特别地, 积分算子)		Approximation by operators (in particular, by integral operators)
41A36	正算子逼近		Approximation by positive operators
41A40	饱和		Saturation
41A44	最佳常数		Best constants
41A45	任意线性表达式的逼近		Approximation by arbitrary linear expressions
41A46	任意非线性表达式逼近; 宽度与熵		Approximation by arbitrary nonlinear expressions; widths and entropy
41A50	最佳逼近, Chebyshev系统		Best approximation, Chebyshev systems
41A52	最佳逼近的唯一性		Uniqueness of best approximation
41A55	近似求积分		Approximate quadratures
41A58	级数展开(例如: Taylor, Lidstone级数, 但非Fourier级数)		Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
41A60	渐近逼近, 渐近展开(最速下降等)[参见30E15]		Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]
41A63	多维问题(还应在这节中至少给出一个其它分类号)		Multidimensional problems (should also be assigned at least one other classification number in this section)
41A65	抽象逼近理论(赋范线性空间及其它抽象空间中的逼近)		Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A80	逼近公式中的余项		Remainders in approximation formulas
41A99	杂题		Miscellaneous topics
42-XX	Euclid空间上的调和分析		Harmonic analysis on Euclidean spaces
42-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
42-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
42-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
42-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
42-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
42-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
42Axx	单变量调和分析		Harmonic analysis in one variable
42A05	三角多项式, 不等式, 极值问题		Trigonometric polynomials, inequalities, extremal problems
42A10	三角逼近		Trigonometric approximation
42A15	三角插值		Trigonometric interpolation
42A16	Fourier系数, 特殊性质函数的Fourier级数, 特殊Fourier级数(自同构理论, 主要见11F30)		Fourier coefficients, Fourier series of functions with special properties, special Fourier series (For automorphic theory, see mainly 11F30)
42A20	Fourier级数与三角级数的收敛性和绝对收敛性		Convergence and absolute convergence of Fourier and trigonometric series
42A24	Fourier级数和三角级数的可求和性和绝对可求和性		Summability and absolute summability of Fourier and trigonometric series
42A32	特殊型三角级数(正系数、单调系数等)		Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
42A38	Fourier与Fourier-Stieltjes变换及其它Fourier型变换		Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42A45	乘子		Multipliers
42A50	共轭函数、共轭级数、奇异积分		Conjugate functions, conjugate series, singular integrals
42A55	三角函数与其它函数的缺项级数; Riesz乘积		Lacunary series of trigonometric and other functions; Riesz products
42A61	概率方法		Probabilistic methods
42A63	三角展开的唯一性, Fourier展开的唯一性, Riemann理论, 局部化		Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A65	函数集的完备性		Completeness of sets of functions
42A70	三角矩问题		Trigonometric moment problems
42A75	经典殆周期函数, 平均周期函数[参见43A60]		Classical almost periodic functions, mean periodic functions [See also 43A60]
42A82	正定函数		Positive definite functions
42A85	卷积, 因子分解		Convolution, factorization
42A99	其它		None of the above, but in this section
42Bxx	多变量调和分析(自同构理论, 主要见11F30)		Harmonic analysis in several variables (For automorphic theory, see mainly 11F30)
42B05	Fourier级数与系数		Fourier series and coefficients
42B08	可(求)和性		Summability
42B10	Fourier与Fourier-Stieltjes变换及其它Fourier型变换		Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B15	乘子		Multipliers
42B20	奇异积分(Calderón-Zygmund等)		Singular integrals (Calderón-Zygmund, etc.)
42B25	极大函数, Littlewood-Paley理论		Maximal functions, Littlewood-Paley theory
42B30	H^p空间		H^p-spaces
42B35	调和分析中的函数空间		Function spaces arising in harmonic analysis
42B37	调和分析与偏微分方程[参见35-XX]		Harmonic analysis and PDE [See also 35-XX]
42B99	其它		None of the above, but in this section
42Cxx	非三角Fourier分析		Nontrigonometric Fourier analysis
42C05	正交函数与多项式, 一般理论[参见33C45, 33C50, 33D45]		Orthogonal functions and polynomials, general theory [See also 33C45, 33C50, 33D45]
42C10	特殊正交函数的Fourier级数(Legendre多项式、Walsh函数等)		Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42C15	一般调和展开, 框架		General harmonic expansions, frames
42C20	其它调和型变换		Other transformations of harmonic type
42C25	正交级数的唯一性与局部化		Uniqueness and localization for orthogonal series
42C30	函数集的完备性		Completeness of sets of functions
42C40	小波与其它特殊系统		Wavelets and other special systems
42C99	其它		None of the above, but in this section
43-XX	抽象调和分析(拓扑与Lie群的其它分析, 见22Exx)		Abstract harmonic analysis (For other analysis on topological and Lie groups, see 22Exx)
43-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
43-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
43-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
43-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
43-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
43-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
43Axx	抽象调和分析(拓扑与Lie群的其它分析, 见22Exx)		Abstract harmonic analysis (For other analysis on topological and Lie groups, see 22Exx)
43A05	群与半群等上的测度		Measures on groups and semigroups, etc.
43A07	群、半群等上的平均; 顺从群		Means on groups, semigroups, etc.; amenable groups
43A10	群、半群等上的测度代数		Measure algebras on groups, semigroups, etc.
43A15	群、半群等上的L^p空间与其它函数空间		L^p-spaces and other function spaces on groups, semigroups, etc.
43A17	有序群上的分析, H^p理论		Analysis on ordered groups, H^p-theory
43A20	群、半群等上的L¹代数		L¹-algebras on groups, semigroups, etc.
43A22	群、半群等上的函数空间的同态与乘子		Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
43A25	局部紧群与其它Abel群上的Fourier与Fourier-Stieltjes变换		Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
43A30	非Abel群与半群等上的Fourier与Fourier-Stieltjes变换		Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43A32	Fourier型其它变换与算子		Other transforms and operators of Fourier type
43A35	群、半群等上的正定函数		Positive definite functions on groups, semigroups, etc.
43A40	特征标群与对偶对象		Character groups and dual objects
43A45	群、半群等上的谱综合		Spectral synthesis on groups, semigroups, etc.
43A46	特殊集(合)(薄集、Kronecker集、Helson集、Ditkin集、Sidon集等)		Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
43A50	Fourier级数与逆变换的收敛性		Convergence of Fourier series and of inverse transforms
43A55	群、半群等上的可(求)和性方法[参见40J05]		Summability methods on groups, semigroups, etc. [See also 40J05]
43A60	群与半群上的殆周期函数及其推广(递归函数、末端函数等); 殆自同构函数		Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
43A62	超群		Hypergroups
43A65	群、半群等的表示[参见22A10, 22A20, 22Dxx, 22E45]		Representations of groups, semigroups, etc. [See also 22A10, 22A20, 22Dxx, 22E45]
43A70	特殊局部紧群与其它Abel群上的分析[参见11R56, 22B05]		Analysis on specific locally compact and other abelian groups [See also 11R56, 22B05]
43A75	特殊紧群的分析		Analysis on specific compact groups
43A77	一般紧群的分析		Analysis on general compact groups
43A80	其它特殊Lie群的分析[参见22Exx]		Analysis on other specific Lie groups [See also 22Exx]
43A85	齐性空间上的分析		Analysis on homogeneous spaces
43A90	球面函数[参见22E45, 22E46, 33C55]		Spherical functions [See also 22E45, 22E46, 33C55]
43A95	范畴方法[参见46Mxx]		Categorical methods [See also 46Mxx]
43A99	其它		None of the above, but in this section
44-XX	积分变换, 运算微积分(分数导数与积分, 见26A33; Fourier变换, 见42A38, 42B10; 分布空间中的积分变换, 见46F12; 数值方法, 见65R10)		Integral transforms, operational calculus (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10)
44-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
44-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
44-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
44-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
44-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
44-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
44Axx	积分变换, 运算微积分(分数导数与积分, 见26A33; Fourier变换, 见42A38, 42B10; 分布空间中的积分变换, 见46F12; 数值方法, 见65R10)		Integral transforms, operational calculus (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10)
44A05	一般变换[参见42A38]		General transforms [See also 42A38]
44A10	Laplace变换		Laplace transform
44A12	Radon变换[参见92C55]		Radon transform [See also 92C55]
44A15	特殊变换(Legendre、Hilbert等)		Special transforms (Legendre, Hilbert, etc.)
44A20	特殊函数的变换		Transforms of special functions
44A30	多重变换		Multiple transforms
44A35	卷积		Convolution
44A40	Mikusiński微积分与其它运算微积分		Calculus of Mikusiński and other operational calculi
44A45	经典运算微积分		Classical operational calculus
44A55	离散运算微积分		Discrete operational calculus
44A60	矩问题		Moment problems
44A99	其它		None of the above, but in this section
45-XX	积分方程		Integral equations
45-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
45-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
45-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
45-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
45-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
45-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
45Axx	线性积分方程		Linear integral equations
45A05	线性积分方程		Linear integral equations
45A99	其它		None of the above, but in this section
45Bxx	Fredholm积分方程		Fredholm integral equations
45B05	Fredholm积分方程		Fredholm integral equations
45B99	其它		None of the above, but in this section
45Cxx	特征值问题[参见34Lxx, 35Pxx, 45P05, 47A75]		Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]
45C05	特征值问题[参见34Lxx, 35Pxx, 45P05, 47A75]		Eigenvalue problems [See also 34Lxx, 35Pxx, 45P05, 47A75]
45C99	其它		None of the above, but in this section
45Dxx	Volterra积分方程[参见34A12]		Volterra integral equations [See also 34A12]
45D05	Volterra积分方程[参见34A12]		Volterra integral equations [See also 34A12]
45D99	其它		None of the above, but in this section
45Exx	奇异积分方程[参见30E20, 30E25, 44A15, 44A35]		Singular integral equations [See also 30E20, 30E25, 44A15, 44A35]
45E05	有Cauchy型核的积分方程[参见35J15]		Integral equations with kernels of Cauchy type [See also 35J15]
45E10	卷积型积分方程(Abel, Picard, Toeplitz和Wiener-Hopf型)[参见47B35]		Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) [See also 47B35]
45E99	其它		None of the above, but in this section
45Fxx	线性积分方程组		Systems of linear integral equations
45F05	非奇异线性积分方程组		Systems of nonsingular linear integral equations
45F10	对偶、三元组等的积分与级数方程		Dual, triple, etc., integral and series equations
45F15	奇异线性积分方程组		Systems of singular linear integral equations
45F99	其它		None of the above, but in this section
45Gxx	非线性积分方程[参见47H30, 47Jxx]		Nonlinear integral equations [See also 47H30, 47Jxx]
45G05	奇异非线性积分方程		Singular nonlinear integral equations
45G10	其它非线性积分方程		Other nonlinear integral equations
45G15	非线性积分方程组		Systems of nonlinear integral equations
45G99	其它		None of the above, but in this section
45Hxx	各种特殊核[参见44A15]		Miscellaneous special kernels [See also 44A15]
45H05	各种特殊核[参见44A15]		Miscellaneous special kernels [See also 44A15]
45H99	其它		None of the above, but in this section
45Jxx	积分-常微分方程[参见34K05, 34K30, 47G20]		Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
45J05	积分-常微分方程[参见34K05, 34K30, 47G20]		Integro-ordinary differential equations [See also 34K05, 34K30, 47G20]
45J99	其它		None of the above, but in this section
45Kxx	积分-偏微分方程[参见34K30, 35R09, 35R10, 47G20]		Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
45K05	积分-偏微分方程[参见34K30, 35R09, 35R10, 47G20]		Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
45K99	其它		None of the above, but in this section
45Lxx	解的理论逼近(数值分析, 见65Rxx)		Theoretical approximation of solutions (For numerical analysis, see 65Rxx)
45L05	解的理论逼近(数值分析, 见65Rxx)		Theoretical approximation of solutions (For numerical analysis, see 65Rxx)
45L99	其它		None of the above, but in this section
45Mxx	定性特性		Qualitative behavior
45M05	渐近性		Asymptotics
45M10	稳定性理论		Stability theory
45M15	周期解		Periodic solutions
45M20	正解		Positive solutions
45M99	其它		None of the above, but in this section
45Nxx	抽象积分方程, 抽象空间中的积分方程		Abstract integral equations, integral equations in abstract spaces
45N05	抽象积分方程, 抽象空间中的积分方程		Abstract integral equations, integral equations in abstract spaces
45N99	其它		None of the above, but in this section
45Pxx	积分算子[参见47B38, 47G10]		Integral operators [See also 47B38, 47G10]
45P05	积分算子[参见47B38, 47G10]		Integral operators [See also 47B38, 47G10]
45P99	其它		None of the above, but in this section
45Qxx	逆问题		Inverse problems
45Q05	逆问题		Inverse problems
45Q99	其它		None of the above, but in this section
45Rxx	随机积分方程[参见60H20]		Random integral equations [See also 60H20]
45R05	随机积分方程[参见60H20]		Random integral equations [See also 60H20]
45R99	其它		None of the above, but in this section
46-XX	泛函分析(拓扑线性空间上的流形模型, 见57Nxx, 58Bxx)		Functional analysis (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx)
46-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
46-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
46-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
46-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
46-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
46-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
46Axx	拓扑线性空间及相关结构(函数空间, 见46Exx)		Topological linear spaces and related structures (For function spaces, see 46Exx)
46A03	局部凸空间的一般理论		General theory of locally convex spaces
46A04	局部凸Fréchet空间与(DF)-空间		Locally convex Fréchet spaces and (DF)-spaces
46A08	桶型空间, 有界型空间		Barrelled spaces, bornological spaces
46A11	紧性或可(求)和性性质确定的空间(核空间、Schwarz空间、Montel空间等)		Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
46A13	用归纳或射影极限(LB、LF等)定义的空间[参见46M40]		Spaces defined by inductive or projective limits (LB, LF, etc.) [See also 46M40]
46A16	非局部凸空间(可度量拓扑线性空间、局部有界空间、拟-Banach空间等)		Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46A17	有界型与相关结构; Mackey收敛等		Bornologies and related structures; Mackey convergence, etc.
46A19	其它“拓扑”线性空间(收敛空间、秩空间、在比R等更一般的有序结构中取值的度量空间等)		Other “topological” linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than R, etc.)
46A20	对偶性理论		Duality theory
46A22	Hahn-Banach型定理; 泛函与算子的扩张及其提升[参见46M10]		Theorems of Hahn-Banach type; extension and lifting of functionals and operators [See also 46M10]
46A25	自反性与半自反性[参见46B10]		Reflexivity and semi-reflexivity [See also 46B10]
46A30	开映射与闭图定理; 完备性(包括B-完备性, B_r-完备性)		Open mapping and closed graph theorems; completeness (including B-, B_r-completeness)
46A32	线性算子空间; 拓扑张量积; 逼近性质[参见46B28, 46M05, 47L05, 47L20]		Spaces of linear operators; topological tensor products; approximation properties [See also 46B28, 46M05, 47L05, 47L20]
46A35	可(求)和性与基[参见46B15]		Summability and bases [See also 46B15]
46A40	有序拓扑线性空间, 向量格[参见06F20, 46B40, 46B42]		Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
46A45	序列空间(包括Köthe序列空间)[参见46B45]		Sequence spaces (including Köthe sequence spaces) [See also 46B45]
46A50	拓扑线性空间的紧性; angelic空间等		Compactness in topological linear spaces; angelic spaces, etc.
46A55	拓扑线性空间中的凸集; Choquet理论[参见52A07]		Convex sets in topological linear spaces; Choquet theory [See also 52A07]
46A61	分次Fréchet空间和驯顺算子		Graded Fréchet spaces and tame operators
46A63	拓扑不变量((DN)、(Ω)等)		Topological invariants ((DN), (Ω), etc.)
46A70	Saks空间及其对偶(严格拓扑、混合拓扑、2范数空间、共Saks空间等)		Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
46A80	模空间		Modular spaces
46A99	其它		None of the above, but in this section
46Bxx	赋范线性空间与Banach空间; Banach格(函数空间, 见46Exx)		Normed linear spaces and Banach spaces; Banach lattices (For function spaces, see 46Exx)
46B03	Banach空间的同构理论(包括重新赋范)		Isomorphic theory (including renorming) of Banach spaces
46B04	Banach空间的等距理论		Isometric theory of Banach spaces
46B06	Banach空间的渐近理论[参见52A23]		Asymptotic theory of Banach spaces [See also 52A23]
46B07	Banach空间的局部理论		Local theory of Banach spaces
46B08	Banach空间理论中的超积法[参见46M07]		Ultraproduct techniques in Banach space theory [See also 46M07]
46B09	Banach空间理论中的概率方法[参见60Bxx]		Probabilistic methods in Banach space theory [See also 60Bxx]
46B10	对偶性与自反性[参见46A25]		Duality and reflexivity [See also 46A25]
46B15	可(求)和性与基[参见46A35]		Summability and bases [See also 46A35]
46B20	赋范线性空间的几何与结构		Geometry and structure of normed linear spaces
46B22	Radon-Nikodym, Krein-Milman及相关性质[参见46G10]		Radon-Nikodym, Krein-Milman and related properties [See also 46G10]
46B25	一般理论的经典Banach空间		Classical Banach spaces in the general theory
46B26	不可分Banach空间		Nonseparable Banach spaces
46B28	算子空间; 张量积; 逼近性质[参见46A32, 46M05, 47L05, 47L20]		Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
46B40	有序赋范空间[参见46A40, 46B42]		Ordered normed spaces [See also 46A40, 46B42]
46B42	Banach格[参见46A40, 46B40]		Banach lattices [See also 46A40, 46B40]
46B45	Banach序列空间[参见46A45]		Banach sequence spaces [See also 46A45]
46B50	Banach(或赋范)空间中的紧性		Compactness in Banach (or normed) spaces
46B70	赋范线性空间之间的插值(法)[参见46M35]		Interpolation between normed linear spaces [See also 46M35]
46B80	Banach空间的非线性分类;非线性商		Nonlinear classification of Banach spaces; nonlinear quotients
46B85	离散度量空间嵌入Banach空间;在拓扑和计算机科学中的应用[参见05C12, 68Rxx]		Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science [See also 05C12, 68Rxx]
46B99	其它		None of the above, but in this section
46Cxx	内积空间及其推广, Hilbert空间(函数空间, 见46Exx)		Inner product spaces and their generalizations, Hilbert spaces (For function spaces, see 46Exx)
46C05	Hilbert与准-Hilbert空间: 几何与拓扑(包括半定内积空间)		Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
46C07	Hilbert子空间(=算子范围); 互补(Aronszajn、de Branges等)[参见46B70, 46M35]		Hilbert subspaces (= operator ranges); complementation (Aronszajn, de Branges, etc.) [See also 46B70, 46M35]
46C15	Hilbert空间的特征		Characterizations of Hilbert spaces
46C20	不定内积空间(Krein空间、Pontryagin空间等)[参见47B50]		Spaces with indefinite inner product (Krein spaces, Pontryagin spaces, etc.) [See also 47B50]
46C50	内积的推广(半内积、偏内积等)		Generalizations of inner products (semi-inner products, partial inner products, etc.)
46C99	其它		None of the above, but in this section
46Exx	线性函数空间及其对偶[参见30H05, 32A38, 46F05](函数代数, 见46J10)		Linear function spaces and their duals [See also 30H05, 32A38, 46F05] (For function algebras, see 46J10)
46E05	连续、可微或解析函数的格		Lattices of continuous, differentiable or analytic functions
46E10	连续、可微或解析函数的拓扑线性空间		Topological linear spaces of continuous, differentiable or analytic functions
46E15	连续、可微或解析函数的Banach空间		Banach spaces of continuous, differentiable or analytic functions
46E20	连续、可微或解析函数的Hilbert空间		Hilbert spaces of continuous, differentiable or analytic functions
46E22	再生核的Hilbert空间(=[真]泛函Hilbert空间)包括de Branges-Rovnyak和其它结构空间)[参见47B32]		Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
46E25	连续、可微或解析函数的环与代数(Banach函数代数, 见46J10, 46J15)		Rings and algebras of continuous, differentiable or analytic functions (For Banach function algebras, see 46J10, 46J15)
46E27	测度空间[参见28A33, 46Gxx]		Spaces of measures [See also 28A33, 46Gxx]
46E30	可测函数空间(L^p空间、Orlicz空间、Köthe函数空间、Lorentz空间、重排不变空间、理想空间等)		Spaces of measurable functions (L^p-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev空间与其它“光滑”函数, 嵌入定理, 迹定理		Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E39	离散变量函数的Sobolev(和相似类的)空间		Sobolev (and similar kinds of) spaces of functions of discrete variables
46E40	向量值与算子值函数空间		Spaces of vector- and operator-valued functions
46E50	无限维空间上可微或全纯函数空间[参见46G20, 46G25, 47H60]		Spaces of differentiable or holomorphic functions on infinite-dimensional spaces [See also 46G20, 46G25, 47H60]
46E99	其它		None of the above, but in this section
46Fxx	分布, 广义函数, 分布空间[参见46T30]		Distributions, generalized functions, distribution spaces [See also 46T30]
46F05	测试函数、分布与超分布的拓扑线性空间[参见46E10, 46E35]		Topological linear spaces of test functions, distributions and ultradistributions [See also 46E10, 46E35]
46F10	带分布的运算		Operations with distributions
46F12	分布空间中的积分变换[参见42-XX, 44-XX]		Integral transforms in distribution spaces [See also 42-XX, 44-XX]
46F15	超函数, 解析泛函[参见32A25, 32A45, 32C35, 58J15]		Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15]
46F20	解析函数边值的分布与超分布[参见30D40, 30E25, 32A40]		Distributions and ultradistributions as boundary values of analytic functions [See also 30D40, 30E25, 32A40]
46F25	无限维空间上的分布[参见58C35]		Distributions on infinite-dimensional spaces [See also 58C35]
46F30	非线性分析的广义函数(Rosinger、Colombeau、非标准等)		Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
46F99	其它		None of the above, but in this section
46Gxx	测度, 积分, 导数, 正则(所有涉及无限维空间)[参见28-XX, 46Txx]		Measures, integration, derivative, holomorphy (all involving infinite-dimensional spaces) [See also 28-XX, 46Txx]
46G05	导数[参见46T20, 58C20, 58C25]		Derivatives [See also 46T20, 58C20, 58C25]
46G10	向量值测度与积分[参见28Bxx, 46B22]		Vector-valued measures and integration [See also 28Bxx, 46B22]
46G12	抽象线性空间上的测度与积分[参见28C20, 46T12]		Measures and integration on abstract linear spaces [See also 28C20, 46T12]
46G15	泛函分析提升理论[参见28A51]		Functional analytic lifting theory [See also 28A51]
46G20	无限维正则[参见32-XX, 46E50, 46T25, 58B12, 58C10]		Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10]
46G25	多重线性映射(的空间), 多项式[参见46E50, 46G20, 47H60]		(Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60]
46G99	其它		None of the above, but in this section
46Hxx	拓扑代数, 赋范环与代数, Banach代数(群代数, 卷积代数与测度代数, 见43A10, 43A20)		Topological algebras, normed rings and algebras, Banach algebras (For group algebras, convolution algebras and measure algebras, see 43A10, 43A20)
46H05	拓扑代数的一般理论		General theory of topological algebras
46H10	理想与子代数		Ideals and subalgebras
46H15	拓扑代数的表示		Representations of topological algebras
46H20	拓扑代数的结构, 分类		Structure, classification of topological algebras
46H25	赋范模与Banach模, 拓扑模(如果不属于13-XX或16-XX)		Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
46H30	拓扑代数中的泛函微积分[参见47A60]		Functional calculus in topological algebras [See also 47A60]
46H35	算子的拓扑代数[主要见47Lxx]		Topological algebras of operators [See mainly 47Lxx]
46H40	自动连续性		Automatic continuity
46H70	非结合拓扑代数[参见46K70, 46L70]		Nonassociative topological algebras [See also 46K70, 46L70]
46H99	其它		None of the above, but in this section
46Jxx	交换Banach代数与交换拓扑代数[参见46E25]		Commutative Banach algebras and commutative topological algebras [See also 46E25]
46J05	交换拓扑代数的一般理论		General theory of commutative topological algebras
46J10	连续函数的Banach代数, 函数代数[参见46E25]		Banach algebras of continuous functions, function algebras [See also 46E25]
46J15	可微函数或解析函数的Banach代数, H^p-空间[参见30H10, 32A35, 32A37, 32A38, 42B30]		Banach algebras of differentiable or analytic functions, H^p-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30]
46J20	理想、极大理想、边界		Ideals, maximal ideals, boundaries
46J25	交换拓扑代数的表示		Representations of commutative topological algebras
46J30	子代数		Subalgebras
46J40	交换拓扑代数的结构, 分类		Structure, classification of commutative topological algebras
46J45	根Banach代数		Radical Banach algebras
46J99	其它		None of the above, but in this section
46Kxx	具有对合的拓扑(环与)代数[参见16W10]		Topological (rings and) algebras with an involution [See also 16W10]
46K05	具有对合的拓扑代数的一般理论		General theory of topological algebras with involution
46K10	具有对合的拓扑代数的表示		Representations of topological algebras with involution
46K15	Hilbert代数		Hilbert algebras
46K50	具有对合代数的非自伴(子)代数		Nonselfadjoint (sub)algebras in algebras with involution
46K70	具有对合的非结合拓扑代数[参见46H70, 46L70]		Nonassociative topological algebras with an involution [See also 46H70, 46L70]
46K99	其它		None of the above, but in this section
46Lxx	自伴算子代数(C^-代数、von Neumann(W^-)代数等)[参见22D25, 47Lxx]		Selfadjoint operator algebras (C^-algebras, von Neumann (W^-) algebras, etc.) [See also 22D25, 47Lxx]
46L05	C^*-代数的一般理论		General theory of C^*-algebras
46L06	C^*-代数的张量积		Tensor products of C^*-algebras
46L07	算子空间和完备有界映射[参见47L25]		Operator spaces and completely bounded maps [See also 47L25]
46L08	C^*-模		C^*-modules
46L09	C^*-代数的自由积		Free products of C^*-algebras
46L10	Von Neumann代数的一般理论		General theory of von Neumann algebras
46L30	状态		States
46L35	C^*-代数的分类		Classifications of C^*-algebras
46L36	因子的分类		Classification of factors
46L37	子因子及其分类		Subfactors and their classification
46L40	自同构		Automorphisms
46L45	C^*-代数的分解理论		Decomposition theory for C^*-algebras
46L51	非交换测度和积分		Noncommutative measure and integration
46L52	非交换函数空间		Noncommutative function spaces
46L53	非交换概率和统计		Noncommutative probability and statistics
46L54	自由概率和自由算子代数		Free probability and free operator algebras
46L55	非交换动力系统[参见28Dxx, 37Kxx, 37Lxx, 54H20]		Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
46L57	C^*-代数的导数、耗散与正半群		Derivations, dissipations and positive semigroups in C^*-algebras
46L60	自伴算子代数在物理中的应用[参见46N50, 46N55, 47L90, 81T05, 82B10, 82C10]		Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
46L65	量化, 形变		Quantizations, deformations
46L70	非结合自伴算子代数[参见46H70, 46K70]		Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]
46L80	K-理论与算子代数(包括循环理论)[参见18F25, 19Kxx, 46M20, 55Rxx, 58J22]		K-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L85	非交换拓扑[参见58B32, 58B34, 58J22]		Noncommutative topology [See also 58B32, 58B34, 58J22]
46L87	非交换微分几何[参见58B32, 58B34, 58J22]		Noncommutative differential geometry [See also 58B32, 58B34, 58J22]
46L89	基于C^*-代数理论的其它“非交换”数学[参见58B32, 58B34, 58J22]		Other “noncommutative” mathematics based on C^*-algebra theory [See also 58B32, 58B34, 58J22]
46L99	其它		None of the above, but in this section
46Mxx	泛函分析中的范畴论方法[参见18-XX]		Methods of category theory in functional analysis [See also 18-XX]
46M05	张量积[参见46A32, 46B28, 47A80]		Tensor products [See also 46A32, 46B28, 47A80]
46M07	超积[参见46B08, 46S20]		Ultraproducts [See also 46B08, 46S20]
46M10	射影与内射对象[参见46A22]		Projective and injective objects [See also 46A22]
46M15	范畴, 函子(K-理论与EXT等, 见19K33, 46L80, 46M18, 46M20)		Categories, functors (For K-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20)
46M18	同调方法(正合序列、右逆、提升等)		Homological methods (exact sequences, right inverses, lifting, etc.)
46M20	代数拓扑方法(上同调、层与丛理论等)[参见14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]		Methods of algebraic topology (cohomology, sheaf and bundle theory, etc.) [See also 14F05, 18Fxx, 19Kxx, 32Cxx, 32Lxx, 46L80, 46M15, 46M18, 55Rxx]
46M35	拓扑向量空间的抽象插值(法)[参见46B70]		Abstract interpolation of topological vector spaces [See also 46B70]
46M40	归纳与射影极限[参见46A13]		Inductive and projective limits [See also 46A13]
46M99	其它		None of the above, but in this section
46Nxx	泛函分析的各种应用[参见47Nxx]		Miscellaneous applications of functional analysis [See also 47Nxx]
46N10	在最优化、凸分析、数学规划、经济方面的应用		Applications in optimization, convex analysis, mathematical programming, economics
46N20	在微分与积分方程中的应用		Applications to differential and integral equations
46N30	在概率论与统计学中的应用		Applications in probability theory and statistics
46N40	在数值分析中的应用[参见65Jxx]		Applications in numerical analysis [See also 65Jxx]
46N50	在量子物理中的应用		Applications in quantum physics
46N55	在统计物理中的应用		Applications in statistical physics
46N60	在生物学与其它科学中的应用		Applications in biology and other sciences
46N99	其它		None of the above, but in this section
46Sxx	泛函分析的其它(非经典)类型[参见47Sxx]		Other (nonclassical) types of functional analysis [See also 47Sxx]
46S10	域上而非R或C或四元数的泛函分析; 非Archimedes泛函分析[参见12J25, 32P05]		Functional analysis over fields other than R or C or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
46S20	非标准泛函分析[参见03H05]		Nonstandard functional analysis [See also 03H05]
46S30	构造性泛函分析[参见03F60]		Constructive functional analysis [See also 03F60]
46S40	模糊泛函分析[参见03E72]		Fuzzy functional analysis [See also 03E72]
46S50	概率度量线性空间中的泛函分析		Functional analysis in probabilistic metric linear spaces
46S60	超空间(超流形)或分次空间上的泛函分析[参见58A50, 58C50]		Functional analysis on superspaces (supermanifolds) or graded spaces [See also 58A50 and 58C50]
46S99	其它		None of the above, but in this section
46Txx	非线性泛函分析[参见47Hxx, 47Jxx, 58Cxx, 58Dxx]		Nonlinear functional analysis [See also 47Hxx, 47Jxx, 58Cxx, 58Dxx]
46T05	无限维流形[参见53Axx, 57N20, 58Bxx, 58Dxx]		Infinite-dimensional manifolds [See also 53Axx, 57N20, 58Bxx, 58Dxx]
46T10	映射的流形		Manifolds of mappings
46T12	流形上的测度(Gauss、圆柱形的等)和积分(Feynman、路径、Fresnel等)[参见28Cxx, 46G12, 60-XX]		Measure (Gaussian, cylindrical, etc.) and integrals (Feynman, path, Fresnel, etc.) on manifolds [See also 28Cxx, 46G12, 60-XX]
46T20	连续和可微映射[参见46G05]		Continuous and differentiable maps [See also 46G05]
46T25	全纯映射[参见46G20]		Holomorphic maps [See also 46G20]
46T30	非线性空间上的分布和广义函数[参见46Fxx]		Distributions and generalized functions on nonlinear spaces [See also 46Fxx]
46T99	其它		None of the above, but in this section
47-XX	算子理论		Operator theory
47-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
47-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
47-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
47-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
47-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
47-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
47Axx	线性算子的一般理论		General theory of linear operators
47A05	一般理论(伴随的、共轭的、乘积、逆、域、值域等)		General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A06	线性关系(多值线性算子)		Linear relations (multivalued linear operators)
47A07	形式(双线性的, 半双线性的, 多线性的)		Forms (bilinear, sesquilinear, multilinear)
47A10	谱, 预解式		Spectrum, resolvent
47A11	局部谱性质		Local spectral properties
47A12	数值值域, 数值半径		Numerical range, numerical radius
47A13	多变量算子理论(谱、Fredholm等)		Several-variable operator theory (spectral, Fredholm, etc.)
47A15	不变子空间[参见47A46]		Invariant subspaces [See also 47A46]
47A16	循环向量, 超循环和混沌算子		Cyclic vector, hypercyclic and chaotic operators
47A20	开拓、扩张、压缩		Dilations, extensions, compressions
47A25	谱集		Spectral sets
47A30	范数(不等式、多范数等)		Norms (inequalities, more than one norm, etc.)
47A35	遍历理论[参见28Dxx, 37Axx]		Ergodic theory [See also 28Dxx, 37Axx]
47A40	散射理论[参见34L25, 35P25, 37K15, 58J50, 81Uxx]		Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx]
47A45	收缩算子与非自伴算子的标准模(型)		Canonical models for contractions and nonselfadjoint operators
47A46	投影或不变子空间的链(套), 沿着链的积分等		Chains (nests) of projections or of invariant subspaces, integrals along chains, etc.
47A48	算子综合(=结点)、vessels、线性系统、特征函数、实现等		Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc.
47A50	未知向量线性算子的方程及不等式		Equations and inequalities involving linear operators, with vector unknowns
47A52	不适定问题, 正则化[参见35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]		Ill-posed problems, regularization [See also 35R25, 47J06, 65F22, 65J20, 65L08, 65M30, 65R30]
47A53	(半)Fredholm算子; 指数理论[参见58B15, 58J20]		(Semi-) Fredholm operators; index theories [See also 58B15, 58J20]
47A55	摄动理论[参见47H14, 58J37, 70H09, 81Q15]		Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15]
47A56	其值是线性算子的函数(算子与矩阵值函数等, 包括解析和亚纯函数)		Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
47A57	插值、矩及扩张问题中的算子方法[参见30E05, 42A70, 42A82, 44A60]		Operator methods in interpolation, moment and extension problems [See also 30E05, 42A70, 42A82, 44A60]
47A58	算子逼近理论		Operator approximation theory
47A60	谓词演算		Functional calculus
47A62	未知算子的线性算子方程		Equations involving linear operators, with operator unknowns
47A63	算子不等式		Operator inequalities
47A64	算子平均、短算子等		Operator means, shorted operators, etc.
47A65	结构理论		Structure theory
47A66	拟三角算子和非拟三角算子, 拟对角算子和非拟对角算子		Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators
47A67	表示理论		Representation theory
47A68	因子分解理论(包括Wiener-Mopf与谱因子分解)		Factorization theory (including Wiener-Hopf and spectral factorizations)
47A70	(广义)特征函数展开; 受控Hilbert空间		(Generalized) eigenfunction expansions; rigged Hilbert spaces
47A75	特征值问题[参见47J10, 49R05]		Eigenvalue problems [See also 47J10, 49R05]
47A80	算子的张量积[参见46M05]		Tensor products of operators [See also 46M05]
47A99	其它		None of the above, but in this section
47Bxx	线性算子的特殊类		Special classes of linear operators
47B06	Riesz算子; 特征值分布; 算子的近似数、算子的s-数、算子的Kolmogorov数、算子的熵数等		Riesz operators; eigenvalue distributions; approximation numbers, s-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47B07	由紧性性质定义的算子		Operators defined by compactness properties
47B10	属于算子理想(核、p-和、Schatten-von Neumann类中等)的算子[参见47L20]		Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]
47B15	Hermite与正规算子(谱测度、谓词演算等)		Hermitian and normal operators (spectral measures, functional calculus, etc.)
47B20	次正规算子、亚正规算子等		Subnormal operators, hyponormal operators, etc.
47B25	对称与自伴算子(无界的)		Symmetric and selfadjoint operators (unbounded)
47B32	再生核Hilbert空间(包括de Branges、de Branges-Rovnyak和其它结构空间 )中算子[参见46E22]		Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
47B33	复合算子		Composition operators
47B34	核算子		Kernel operators
47B35	Toeplitz算子, Hankel算子, Wiener-Hopf算子[参见45P05, 47G10; 其它积分算子, 参见32A25, 32M15]		Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
47B36	Jacobi(三对角)算子(矩阵)和推广		Jacobi (tridiagonal) operators (matrices) and generalizations
47B37	特殊空间上的算子(加权位移、序列空间上的算子等)		Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47B38	函数空间上的算子(一般理论)		Operators on function spaces (general)
47B39	差分算子[参见39A70]		Difference operators [See also 39A70]
47B40	谱算子、可分解算子、良有界算子等		Spectral operators, decomposable operators, well-bounded operators, etc.
47B44	增生算子、散逸型算子等		Accretive operators, dissipative operators, etc.
47B47	换位子、求导、初等算子等		Commutators, derivations, elementary operators, etc.
47B48	Banach代数上的算子		Operators on Banach algebras
47B49	变换器, 保持(算子空间上的算子)		Transformers, preservers (operators on spaces of operators)
47B50	不定度量空间上的算子[参见46C50]		Operators on spaces with an indefinite metric [See also 46C50]
47B60	有序空间上的算子		Operators on ordered spaces
47B65	正算子和有序有界算子		Positive operators and order-bounded operators
47B80	随机算子[参见47H40, 60H25]		Random operators [See also 47H40, 60H25]
47B99	其它		None of the above, but in this section
47Cxx	作为代数系统元(素)的单线性算子		Individual linear operators as elements of algebraic systems
47C05	代数中的算子		Operators in algebras
47C10	*-代数中的算子		Operators in *-algebras
47C15	C^*-或von Neumann代数中的算子		Operators in C^*- or von Neumann algebras
47C99	其它		None of the above, but in this section
47Dxx	线性算子的群和半群, 及其推广和应用		Groups and semigroups of linear operators, their generalizations and applications
47D03	线性算子的群和半群(非线性算子, 见47H20; 也见20M20)		Groups and semigroups of linear operators (For nonlinear operators, see 47H20; see also 20M20)
47D06	单参数半群与线性发展方程[参见34G10, 34K30]		One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
47D07	Markov半群及在扩散过程中的应用(Markov过程, 见60Jxx)		Markov semigroups and applications to diffusion processes (For Markov processes, see 60Jxx)
47D08	Schrödinger和Feynman-Kac半群		Schrödinger and Feynman-Kac semigroups
47D09	算子正弦及余弦函数与高阶Cauchy问题[参见34G10]		Operator sine and cosine functions and higher-order Cauchy problems [See also 34G10]
47D60	C-半群, 正则半群		C-semigroups, regularized semigroups
47D62	积分半群		Integrated semigroups
47D99	其它		None of the above, but in this section
47Exx	常微分算子[参见34Bxx, 34Lxx]		Ordinary differential operators [See also 34Bxx, 34Lxx]
47E05	常微分算子[参见34Bxx, 34Lxx](还必须在47-XX中至少指定一个其它分类号）		Ordinary differential operators [See also 34Bxx, 34Lxx](should also be assigned at least one other classification number in section 47)
47E99	其它		None of the above, but in this section
47Fxx	偏微分算子[参见35Pxx, 58Jxx]		Partial differential operators [See also 35Pxx, 58Jxx]
47F05	偏微分算子[参见35Pxx, 58Jxx](还必须在47-XX中至少指定一个其它分类号)		Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)
47F99	其它		None of the above, but in this section
47Gxx	积分算子, 积分-微分算子与伪微分算子[参见58Jxx]		Integral, integro-differential, and pseudodifferential operators [See also 58Jxx]
47G10	积分算子[参见45P05]		Integral operators [See also 45P05]
47G20	积分-微分算子[参见34K30, 35R09, 35R10, 45Jxx, 45Kxx]		Integro-differential operators [See also 34K30, 35R09, 35R10, 45Jxx, 45Kxx]
47G30	伪微分算子[参见35Sxx, 58Jxx]		Pseudodifferential operators [See also 35Sxx, 58Jxx]
47G40	位势算子[参见31-XX]		Potential operators [See also 31-XX]
47G99	其它		None of the above, but in this section
47Hxx	非线性算子及其性质(整体及几何方面, 见49J53, 58-XX, 特别地, 见58Cxx)		Nonlinear operators and their properties (For global and geometric aspects, see 49J53, 58-XX, especially 58Cxx)
47H04	集值算子[参见28B20, 54C60, 58C06]		Set-valued operators [See also 28B20, 54C60, 58C06]
47H05	单调算子和推广		Monotone operators and generalizatios
47H06	增生算子、耗散算子等		Accretive operators, dissipative operators, etc.
47H07	在有序Banach空间或其它有序拓扑向量空间上的单调算子及正算子		Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H08	非紧性测度和凝聚映射、K-集压缩等		Measures of noncompactness and condensing mappings, K-set contractions, etc.
47H09	压缩型映射、非扩张映射、A真映射等		Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
47H10	不动点定理[参见37C25, 54H25, 55M20, 58C30]		Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
47H11	度理论[参见55M25, 58C30]		Degree theory [See also 55M25, 58C30]
47H14	非线性算子的摄动[参见47A55, 58J37, 70H09, 70K60, 81Q51]		Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q51]
47H20	非线性算子半群[参见37L05, 47J35, 54H15, 58D07]		Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07]
47H25	非线性遍历定理[参见28Dxx, 37Axx, 47A35]		Nonlinear ergodic theorems [See also 28Dxx, 37Axx, 47A35]
47H30	特殊非线性算子(叠加算子、Hammerstein算子、Nemytskiǐ算子、Uryson算子等)[参见45Gxx, 45P05]		Particular nonlinear operators (superposition, Hammerstein, Nemytskiǐ, Uryson, etc.) [See also 45Gxx, 45P05]
47H40	随机算子[参见47B80, 60H25]		Random operators [See also 47B80, 60H25]
47H60	多线性和多项式算子[参见46G25]		Multilinear and polynomial operators [See also 46G25]
47H99	其它		None of the above, but in this section
47Jxx	涉及非线性算子的方程和不等式[参见46Txx](全局和几何方面, 见58-XX)		Equations and inequalities involving nonlinear operators [See also 46Txx] (For global and geometric aspects, see 58-XX)
47J05	涉及非线性算子的方程(一般理论)[参见47H10, 47J25]		Equations involving nonlinear operators (general) [See also 47H10, 47J25]
47J06	非线性不适定问题[参见35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]		Nonlinear ill-posed problems [See also 35R25, 47A52, 65F22, 65J20, 65L08, 65M30, 65R30]
47J07	抽象逆映射和隐函数定理[参见46T20, 58C15]		Abstract inverse mapping and implicit function theorems [See also 46T20 and 58C15]
47J10	非线性谱理论, 非线性特征值问题[参见49R05]		Nonlinear spectral theory, nonlinear eigenvalue problems [See also 49R05]
47J15	抽象分歧理论[参见34C23, 37Gxx, 58E07, 58E09]		Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09]
47J20	涉及非线性算子的变分和不等式的其它类型(一般理论)[参见49J40]		Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40]
47J22	包含变分和其它类型[参见34A60, 49J21, 49K21]		Variational and other types of inclusions [See also 34A60, 49J21, 49K21]
47J25	迭代过程[参见65J15]		Iterative procedures [See also 65J15]
47J30	变分法[参见58Exx]		Variational methods [See also 58Exx]
47J35	非线性发展方程[参见34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]		Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]
47J40	具有滞后算子的方程[参见34C55, 74N30]		Equations with hysteresis operators [See also 34C55, 74N30]
47J99	其它		None of the above, but in this section
47Lxx	算子的线性空间和代数[参见46Lxx]		Linear spaces and algebras of operators [See also 46Lxx]
47L05	算子的线性空间[参见46A32和46B28]		Linear spaces of operators [See also 46A32 and 46B28]
47L07	算子的凸集和锥[参见46A55]		Convex sets and cones of operators [See also 46A55]
47L10	Banach空间和其它拓扑线性空间上算子的代数		Algebras of operators on Banach spaces and other topological linear spaces
47L15	具有符号结构的算子代数		Operator algebras with symbol structure
47L20	算子理想[参见47B10]		Operator ideals [See also 47B10]
47L22	多项式理想及多线性映射的理想		Ideals of polynomials and of multilinear mappings
47L25	算子空间(=矩阵赋范空间)[参见46L07]		Operator spaces (= matricially normed spaces) [See also 46L07]
47L30	Hilbert空间上的抽象算子代数		Abstract operator algebras on Hilbert spaces
47L35	套代数, CSL代数		Nest algebras, CSL algebras
47L40	极限代数, C^*代数的子代数		Limit algebras, subalgebras of C^*-algebras
47L45	对偶代数; 弱闭单生成算子代数		Dual algebras; weakly closed singly generated operator algebras
47L50	算子代数的对偶空间		Dual spaces of operator algebras
47L55	(非自伴)算子代数的表示		Representations of (nonselfadjoint) operator algebras
47L60	无界算子的代数; 算子的偏代数		Algebras of unbounded operators; partial algebras of operators
47L65	叉积代数(解析叉积)		Crossed product algebras (analytic crossed products)
47L70	非结合非自伴算子代数		Nonassociative nonselfadjoint operator algebras
47L75	其它非自伴算子代数		Other nonselfadjoint operator algebras
47L80	特殊型算子(Toeplitz、积分、伪微分等)的代数		Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)
47L90	算子代数应用于物理		Applications of operator algebras to physics
47L99	其它		None of the above, but in this section
47Nxx	算子理论的各种应用[参见46Nxx]		Miscellaneous applications of operator theory [See also 46Nxx]
47N10	在最优化、凸分析、数学规划、经济中的应用		Applications in optimization, convex analysis, mathematical programming, economics
47N20	在微分与积分方程中的应用		Applications to differential and integral equations
47N30	在概率论与统计学中的应用		Applications in probability theory and statistics
47N40	在数值分析中的应用[参见65Jxx]		Applications in numerical analysis [See also 65Jxx]
47N50	在物理科学中的应用		Applications in physics sciences
47N60	在化学和生命科学中的应用		Applications in chemistry and life sciences
47N70	在系统论、回路和控制论中的应用		Applications in systems theory, circuits, and control theory
47N99	其它		None of the above, but in this section
47Sxx	算子理论的其它(非经典)类型[参见46Sxx]		Other (nonclassical) types of operator theory [See also 46Sxx]
47S10	域上而非R或C或四元数上的算子理论; 非Archimedes算子理论		Operator theory over fields other than R, C or the quaternions; non-Archimedean operator theory
47S20	非标准算子理论[参见03H05]		Nonstandard operator theory [See also 03H05]
47S30	构造性算子理论[参见03F60]		Constructive operator theory [See also 03F60]
47S40	模糊算子理论[参见03E72]		Fuzzy operator theory [See also 03E72]
47S50	概率度量线性空间中的算子理论[参见54E70]		Operator theory in probabilistic metric linear spaces [See also 54E70]
47S99	其它		None of the above, but in this section
49-XX	变分法与最优控制; 最优化[参见34H05, 34K35, 65Kxx, 90Cxx, 93-XX]		Calculus of variations and optimal control; optimization [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
49-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
49-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
49-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
49-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
49-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
49-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
49Jxx	存在性理论		Existence theories
49J05	一个独立变量的自由问题		Free problems in one independent variable
49J10	两个或更多独立变量的自由问题		Free problems in two or more independent variables
49J15	涉及常微分方程的最优控制问题		Optimal control problems involving ordinary differential equations
49J20	涉及偏微分方程的最优控制问题		Optimal control problems involving partial differential equations
49J21	涉及非微分方程关系的最优控制问题		Optimal control problems involving relations other than differential equations
49J27	抽象空间中的问题[参见90C48, 93C25]		Problems in abstract spaces [See also 90C48, 93C25]
49J30	属于约束类(Lipschitz控制、开关式控制等)的最优解		Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49J35	极小极大问题		Minimax problems
49J40	涉及变分不等式的变分法[参见47J20]		Variational methods including variational inequalities [See also 47J20]
49J45	涉及半连续性与收敛性问题的方法; 松弛		Methods involving semicontinuity and convergence; relaxation
49J50	Fréchet与Gateaux可微性[参见46G05, 58C20]		Fréchet and Gateaux differentiability [See also 46G05, 58C20]
49J52	非光滑分析[参见46G05, 58C50]		Nonsmooth analysis [See also 46G05, 58C50]
49J53	集值和变分分析[参见28B20, 47H04, 54C60, 58C06]		Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06]
49J55	涉及随机性的问题[参见93E20]		Problems involving randomness [See also 93E20]
49J99	其它		None of the above, but in this section
49Kxx	最优性的条件		optimality conditions
49K05	一个独立变量的自由问题		Free problems in one independent variable
49K10	两个或更多独立变量的自由问题		Free problems in two or more independent variables
49K15	涉及常微分方程的问题		Problems involving ordinary differential equations
49K20	涉及偏微分方程的问题		Problems involving partial differential equations
49K21	涉及非微分方程关系的问题		Problems involving relations other than differential equations
49K27	抽象空间中的问题[参见90C48, 93C25]		Problems in abstract spaces [See also 90C48, 93C25]
49K30	属于约束类的最优解		Optimal solutions belonging to restricted classes
49K35	极小极大问题		Minimax problems
49K40	灵敏度, 稳定性, 适定性[参见90C31]		Sensitivity, stability, well-posedness [See also 90C31]
49K45	涉及随机性的问题[参见93E20]		Problems involving randomness [See also 93E20]
49K99	其它		None of the above, but in this section
49Lxx	Hamilton-Jacobi理论, 包括动态规划		Hamilton-Jacobi theories, including dynamic programming
49L20	动态规划方法		Dynamic programming method
49L25	粘性解		Viscosity solutions
49L99	其它		None of the above, but in this section
49Mxx	数值方法[参见90Cxx, 65Kxx]		Numerical methods [See also 90Cxx, 65Kxx]
49M05	建立在必要条件上的方法		Methods based on necessary conditions
49M15	Newton型方法		Newton-type methods
49M20	松弛型法		Methods of relaxation type
49M25	离散逼近		Discrete approximations
49M27	分解法		Decomposition methods
49M29	涉及对偶性的方法		Methods involving duality
49M30	其它方法		Other methods
49M37	非线性规划型方法[参见90C30, 65Kxx]		Methods of nonlinear programming type [See also 90C30, 65Kxx]
49M99	其它		None of the above, but in this section
49Nxx	杂题		Miscellaneous topics
49N05	线性最优控制问题[参见93C05]		Linear optimal control problems [See also 93C05]
49N10	线性-二次问题		Linear-quadratic problems
49N15	对偶性理论		Duality theory
49N20	周期最优化		Periodic optimization
49N25	脉冲最优控制问题		Impulsive optimal control problems
49N30	不完全信息问题[参见93C41]		Problems with incomplete information [See also 93C41]
49N35	最优反馈综合法[参见93B52]		Optimal feedback synthesis [See also 93B52]
49N45	逆问题		Inverse problems
49N60	解的正则性		Regularity of solutions
49N70	微分对策		Differential games
49N75	追逃对策		Pursuit and evasion games
49N90	最优控制和微分对策的应用[参见90C90, 93C95]		Applications of optimal control and differential games [See also 90C90, 93C95]
49N99	其它		None of the above, but in this section
49Qxx	流形[参见58Exx]		Manifolds [See also 58Exx]
49Q05	极小曲面[参见53A10, 58E12]		Minimal surfaces [See also 53A10, 58E12]
49Q10	形状而非极小曲面的最优化[参见90C90]		Optimization of shapes other than minimal surfaces [See also 90C90]
49Q12	灵敏度分析		Sensitivity analysis
49Q15	几何测度与积分理论, 积分与正规流[参见28A75, 32C30, 58A25, 58C35]		Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]
49Q20	几何测度理论合并中的变分问题		Variational problems in a geometric measure-theoretic setting
49Q99	其它		None of the above, but in this section
49Rxx	算子特征值的变分法[参见47A75]		Variational methods for eigenvalues of operators [See also 47A75]
49R05	算子特征值的变分法[参见47A75](还必须在49-XX中至少指定一个其它分类号)		Variational methods for eigenvalues of operators [See also 47A75] (should also be assigned at least one other classification number in Section 49)
49R99	其它		None of the above, but in this section
49Sxx	物理学的变分原理		Variational principle of physics
49S05	物理学的变分原理(还必须在49-XX中至少指定一个其它分类号）		Variational principle of physics(should also be assigned at least one other classification number in Section 49)
49S99	其它		None of the above, but in this section
51-XX	几何学(代数几何, 见14-XX)		Geometry (For algebraic geometry, see 14-XX)
51-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
51-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
51-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
51-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
51-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
51-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
51Axx	线性关联几何		Linear incidence geometry
51A05	一般理论及射影几何		General theory and projective geometries
51A10	同态, 自同构与对偶性		Homomorphism, automorphism and dualities
51A15	平行性结构		Structures with parallelism
51A20	构形定理		Configuration theorems
51A25	代数化[参见12Kxx, 20N05]		Algebraization [See also 12Kxx, 20N05]
51A30	Desargues和Pappus几何		Desarguesian and Pappian geometries
51A35	非Desargues仿射与射影平面		Non-Desarguesian affine and projective planes
51A40	平移平面与展形		Translation planes and spreads
51A45	可嵌入射影几何的关联结构		Incidence structures imbeddable into projective geometries
51A50	(配)极几何、辛空间、正交空间		Polar geometry, symplectic spaces, orthogonal spaces
51A99	其它		None of the above, but in this section
51Bxx	非线性关联几何		Nonlinear incidence geometry
51B05	一般理论		General theory
51B10	Möbius几何		Möbius geometries
51B15	Laguerre几何		Laguerre geometries
51B20	Minkowski几何		Minkowski geometries
51B25	Lie几何		Lie geometries
51B99	其它		None of the above, but in this section
51Cxx	环几何(Hjelmslev、Barbilian等)		Ring geometry (Hjelmslev, Barbilian, etc.)
51C05	环几何(Hjelmslev、Barbilian等)		Ring geometry (Hjelmslev, Barbilian, etc.)
51C99	其它		None of the above, but in this section
51Dxx	几何闭包系统		Geometric closure systems
51D05	抽象(Maeda)几何		Abstract (Maeda) geometries
51D10	有交换公理的抽象几何		Abstract geometries with exchange axiom
51D15	有平行性的抽象几何		Abstract geometries with parallelism
51D20	组合几何[参见05B25, 05B35]		Combinatorial geometries [See also 05B25, 05B35]
51D25	子空间的格[参见05B35]		Lattices of subspaces [See also 05B35]
51D30	连续几何与相关论题[参见06Cxx]		Continuous geometries and related topics [See also 06Cxx]
51D99	其它		None of the above, but in this section
51Exx	有限几何与特殊关联结构		Finite geometry and special incidence structures
51E05	一般区组设计[参见05B05]		General block designs [See also 05B05]
51E10	Steiner系统		Steiner systems
51E12	广义四边形, 广义多边形		Generalized quadrangles, generalized polygons
51E14	有限部分几何(一般理论), 网, 部分展形		Finite partial geometries (general), nets, partial spreads
51E15	仿射与射影平面		Affine and projective planes
51E20	有限射影空间中的组合结构[参见05Bxx]		Combinatorial structures in finite projective spaces [See also 05Bxx]
51E21	块集, 卵形线, k-弧		Blocking sets, ovals, k-arcs
51E22	Galois空间中的线性码与caps[参见94B05]		Linear codes and caps in Galois spaces [See also 94B05]
51E23	展形与填装问题		Spreads and packing problems
51E24	图的造型与图的几何		Buildings and the geometry of diagrams
51E25	其它有限非线性几何		Other finite nonlinear geometries
51E26	其它有限线性几何		Other finite linear geometries
51E30	其它有限关联结构[参见05B30]		Other finite incidence structures [See also 05B30]
51E99	其它		None of the above, but in this section
51Fxx	度量几何		Metric geometry
51F05	绝对平面		Absolute planes
51F10	绝对空间		Absolute spaces
51F15	反射群, 反射几何[参见20H10, 20H15; Coxeter群, 见20F55]		Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]
51F20	同余与正交性[参见20H05]		Congruence and orthogonality [See also 20H05]
51F25	正交群与酉群[参见20H05]		Orthogonal and unitary groups [See also 20H05]
51F99	其它		None of the above, but in this section
51Gxx	有序几何(有序关联结构等)		Ordered geometries (ordered incidence structures, etc.)
51G05	有序几何(有序关联结构等)		Ordered geometries (ordered incidence structures, etc.)
51G99	其它		None of the above, but in this section
51Hxx	拓扑几何		Topological geometry
51H05	一般理论		General theory
51H10	拓扑线性关联结构		Topological linear incidence structures
51H15	拓扑非线性关联结构		Topological nonlinear incidence structures
51H20	流形上的拓扑几何[参见57-XX]		Topological geometries on manifolds [See also 57-XX]
51H25	具有可微结构的几何[参见53Cxx, 53C70]		Geometries with differentiable structure [See also 53Cxx, 53C70]
51H30	具有代数流形结构的几何[参见14-XX]		Geometries with algebraic manifold structure [See also 14-XX]
51H99	其它		None of the above, but in this section
51Jxx	关联群		Incidence groups
51J05	一般理论		General theory
51J10	射影关联群		Projective incidence groups
51J15	运动空间		Kinematic spaces
51J20	拟域与拟代数表示[参见12K05, 16Y30]		Representation by near-fields and near-algebras [See also 12K05, 16Y30]
51J99	其它		None of the above, but in this section
51Kxx	距离几何		Distance geometry
51K05	一般理论		General theory
51K10	综合微分几何		Synthetic differential geometry
51K99	其它		None of the above, but in this section
51Lxx	几何有序结构[参见53C75]		Geometric order structures [See also 53C75]
51L05	不可微曲线的序几何		Geometry of orders of nondifferentiable curves
51L10	直接可微曲线		Directly differentiable curves
51L15	通过直接法的n极点定理		n-vertex theorems via direct methods
51L20	曲面的序几何		Geometry of orders of surfaces
51L99	其它		None of the above, but in this section
51Mxx	实几何与复几何		Real and complex geometry
51M04	Euclid几何中的基本问题		Elementary problems in Euclidean geometries
51M05	Euclid几何(一般问题)及其推广		Euclidean geometries (general) and generalizations
51M09	双曲几何与椭圆几何中的基本问题		Elementary problems in hyperbolic and elliptic geometries
51M10	双曲几何与椭圆几何(一般问题)及其推广		Hyperbolic and elliptic geometries (general) and generalizations
51M15	几何构造		Geometric constructions
51M16	不等式与极值问题(凸问题, 见52A40)		Inequalities and extremum problems (For convex problems, see 52A40)
51M20	多面体与多胞形; 正则图, 空间除法[参见51F15]		Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
51M25	长度、面积与体积[参见26B15]		Length, area and volume [See also 26B15]
51M30	线几何及其推广[参见53A25]		Line geometries and their generalizations [See also 53A25]
51M35	射影几何中基本流形的综合处理(Grassmannians, Veronesians及其推广)[参见14M15]		Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]
51M99	其它		None of the above, but in this section
51Nxx	解析几何与画法几何		Analytic and descriptive geometry
51N05	画法几何[参见65D17, 68U07]		Descriptive geometry [See also 65D17, 68U07]
51N10	仿射解析几何		Affine analytic geometry
51N15	射影解析几何		Projective analytic geometry
51N20	Euclid解析几何		Euclidean analytic geometry
51N25	具有其它变换群的解析几何		Analytic geometry with other transformation groups
51N30	经典群几何[参见20Gxx, 14L35]		Geometry of classical groups [See also 20Gxx, 14L35]
51N35	经典代数几何问题[参见14Nxx]		Questions of classical algebraic geometry [See also 14Nxx]
51N99	其它		None of the above, but in this section
51Pxx	几何与物理学(还应在70-XX至86-XX部分至少指定一个分类号)		Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)
51P05	几何与物理学(还应在70-XX至86-XX部分至少指定一个分类号)		Geometry and physics (should also be assigned at least one other classification number from Sections 70-86)
51P99	其它		None of the above, but in this section
52-XX	凸几何与离散几何		Convex and discrete geometry
52-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
52-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
52-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
52-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
52-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
52-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
52Axx	一般凸性		General convexity
52A01	公理化与广义凸性		Axiomatic and generalized convexity
52A05	没有维数约束的凸集		Convex sets without dimension restrictions
52A07	拓扑向量空间中的凸集[参见46A55]		Convex sets in topological vector spaces [See also 46A55]
52A10	2维凸集(包括凸曲线)[参见53A04]		Convex sets in 2 dimensions (including convex curves) [See also 53A04]
52A15	3维凸集(包括凸曲面)[参见53A05, 53C45]		Convex sets in 3 dimensions (including convex surfaces) [See also 53A05, 53C45]
52A20	n维凸集(包括凸超曲面)[参见53A07, 53C45]		Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
52A21	有限维Banach空间(包括特殊范数、高维环面等)[参见46Bxx]		Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
52A22	随机凸集与积分几何[参见53C65, 60D05]		Random convex sets and integral geometry [See also 53C65, 60D05]
52A23	凸体渐近论[参见46B06]		Asymptotic theory of convex bodies [See also 46B06]
52A27	用凸集逼近		Approximation by convex sets
52A30	凸集的变量(星形的、(m, n)-凸等)		Variants of convex sets (star-shaped, (m, n)-convex, etc.)
52A35	Helly型定理与几何横截理论		Helly-type theorems and geometric transversal theory
52A37	组合凸性的其它问题		Other problems of combinatorial convexity
52A38	长度、面积、体积[参见26B15, 28A75, 49Q20]		Length, area, volume [See also 26B15, 28A75, 49Q20]
52A39	混合体积及相关论题		Mixed volumes and related topics
52A40	不等式与极值问题		Inequalities and extremum problems
52A41	凸函数与凸规划[参见26B25, 90C25]		Convex functions and convex programs [See also 26B25, 90C25]
52A55	球面与双曲凸性		Spherical and hyperbolic convexity
52A99	其它		None of the above, but in this section
52Bxx	多胞形与多面体		Polytopes and polyhedra
52B05	组合性质(面数、最短路径等)[参见05Cxx]		Combinatorial properties (number of faces, shortest paths, etc.) [See also 05Cxx]
52B10	三维多胞形		Three-dimensional polytopes
52B11	n-维多胞形		n-dimensional polytopes
52B12	特殊多胞形(线性规划、中心对称等)		Special polytopes (linear programming, centrally symmetric, etc.)
52B15	多胞形的对称性质		Symmetry properties of polytopes
52B20	格多胞形(包括与交换代数及代数几何的关系)[参见06A11, 13F20, 13Hxx]		Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
52B22	Shellability		Shellability
52B35	Gale与其它图(表)		Gale and other diagrams
52B40	拟阵(在凸多胞形前后关系中的实现、组合结构中的凸性等)[参见05B35, 52Cxx]		Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
52B45	剖分与赋值(Hilbert第三问题等)		Dissections and valuations (Hilbert’s third problem, etc.)
52B55	关于凸性的计算方面(计算几何与算法, 见68Q25, 68U05; 数值算法, 见65Yxx)[参见68Uxx]		Computational aspects related to convexity (For computational geometry and algorithms, see 68Q25, 68U05; for numerical algorithms, see 65Yxx) [See also 68Uxx]
52B60	多胞形的等周问题		Isoperimetric problems for polytopes
52B70	多面体流形		Polyhedral manifolds
52B99	其它		None of the above, but in this section
52Cxx	离散几何		Discrete geometry
52C05	格与2维凸体[参见11H06, 11H31, 11P21]		Lattices and convex bodies in 2 dimensions [See also 11H06, 11H31, 11P21]
52C07	格与n维凸体[参见11H06, 11H31, 11P21]		Lattices and convex bodies in n dimensions [See also 11H06, 11H31, 11P21]
52C10	Erdös问题与离散几何的相关论题[参见11Hxx]		Erdös problems and related topics of discrete geometry [See also 11Hxx]
52C15	填装与2维覆盖[参见05B40, 11H31]		Packing and covering in 2 dimensions [See also 05B40, 11H31]
52C17	填装与n维覆盖[参见05B40, 11H31]		Packing and covering in n dimensions [See also 05B40, 11H31]
52C20	2维贴砖[参见05B45, 51M20]		Tilings in 2 dimensions [See also 05B45, 51M20]
52C22	n维贴砖[参见05B45, 51M20]		Tilings in n dimensions [See also 05B45, 51M20]
52C23	拟晶体、非周期贴砖		Quasicrystals, aperiodic tilings
52C25	结构的刚性及挠性[参见70B15]		Rigidity and flexibility of structures [See also 70B15]
52C26	圆填装和离散共形几何		Circle packings and discrete conformal geometry
52C30	线(边)和伪线(伪边)的平面排列		Planar arrangements of lines and pseudolines
52C35	点, 平坦, 超平面的排列[参见32S22]		Arrangements of points, flats, hyperplanes [See also 32S22]
52C40	定向拟阵		Oriented matroids
52C45	几何结构的组合复杂性[参见68U05]		Combinatorial complexity of geometric structures [See also 68U05]
52C99	其它		None of the above, but in this section
53-XX	微分几何(微分拓扑, 见57Rxx; 可微流形的基础问题, 见58Axx)		Differential geometry (For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx)
53-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
53-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
53-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
53-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
53-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
53-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
53Axx	经典微分几何		Classical differential geometry
53A04	Euclid空间中的曲线		Curves in Euclidean space
53A05	Euclid空间中的曲面		Surfaces in Euclidean space
53A07	Euclid n维空间中的高维及高余维曲面		Higher-dimensional and -codimensional surfaces in Euclidean n-space
53A10	极小曲面、具有指定平均曲率的曲面[参见49Q05, 49Q10, 53C42]		Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42]
53A15	仿射微分几何		Affine differential geometry
53A17	运动学		Kinematics
53A20	射影微分几何		Projective differential geometry
53A25	微分线几何		Differential line geometry
53A30	共形微分几何		Conformal differential geometry
53A35	非Euclid微分几何		Non-Euclidean differential geometry
53A40	其它特殊微分几何		Other special differential geometries
53A45	向量与张量分析		Vector and tensor analysis
53A55	微分不变量(局部理论), 几何对象		Differential invariants (local theory), geometric objects
53A60	罗几何[参见14C21, 20N05]		Geometry of webs [See also 14C21, 20N05]
53A99	其它		None of the above, but in this section
53Bxx	局部微分几何		Local differential geometry
53B05	线性和仿射联络		Linear and affine connections
53B10	射影联络		Projective connections
53B15	其它联络		Other connections
53B20	局部Riemann几何		Local Riemannian geometry
53B21	Riemann几何方法		Methods of Riemannian geometry
53B25	局部子流形[参见53C40]		Local submanifolds [See also 53C40]
53B30	Lorentz度量, 不定度量		Lorentz metrics, indefinite metrics
53B35	Hermite和Kähler结构[参见32Cxx]		Hermitian and Kählerian structures [See also 32Cxx]
53B40	Finsler空间和推广(面积度量)		Finsler spaces and generalizations (areal metrics)
53B50	在物理上的应用		Applications to physics
53B99	其它		None of the above, but in this section
53Cxx	整体微分几何[参见51H25, 58-XX](相关丛理论, 见55Rxx, 57Rxx)		Global differential geometry [See also 51H25, 58-XX] (For related bundle theory, see 55Rxx, 57Rxx)
53C05	联络, 一般理论		Connections, general theory
53C07	向量丛(Hermite-Einstein-Yang-Mills)上的特殊联络和度量[参见32Q20]		Special connections and metrics on vector bundles (Hermite-Einstein-Yang-Mills) [See also 32Q20]
53C08	Gerbes, 微分特征标: 微分几何方面		Gerbes, differential characters: differential geometric aspects
53C10	G-结构		G-structures
53C12	叶状结构物(微分几何方面)[参见57R30, 57R32]		Foliations (differential geometric aspects) [See also 57R30, 57R32]
53C15	流形上的一般几何结构(殆复结构、殆积结构等)		General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C17	子Riemann几何		Sub-Riemannian geometry
53C20	整体Riemann几何, 包括扭[参见31C12, 58B20]		Global Riemannian geometry, including pinching [See also 31C12, 58B20]
53C21	Riemann几何方法, 包括偏微分方程方法; 曲率限制[参见58J60]		Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
53C22	测地线[参见58E10]		Geodesics [See also 58E10]
53C23	整体几何和拓扑方法(属于Gromov); 度量空间上的微分几何分析		Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
53C24	刚性结果		Rigidity results
53C25	特殊Riemann流形(Einstein、Sasaki等)		Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C26	超Kähler和四元数Kähler几何, “特殊”几何		Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C27	自旋和自旋^c几何		Spin and Spin^c geometry
53C28	扭子方法[参见32L25]		Twistor methods [See also 32L25]
53C29	完整的问题		Issues of holonomy
53C30	齐次流形[参见14M15, 14M17, 32M10, 57T15]		Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15]
53C35	对称空间[参见32M15, 57T15]		Symmetric spaces [See also 32M15, 57T15]
53C38	校准和校准几何		Calibrations and calibrated geometries
53C40	整体子流形[参见53B25]		Global submanifolds [See also 53B25]
53C42	浸入(极小曲率、规定曲率、紧密的等)[参见49Q05, 49Q10, 53A10, 57R40, 57R42]		Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
53C43	调和映射的微分几何方面[参见58E20]		Differential geometric aspects of harmonic maps [See also 58E20]
53C44	几何发展方程(平均曲率流、Ricci流等)		Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
53C45	整体曲面论(凸曲面属于A.D.Aleksandrov)		Global surface theory (convex surfaces à la A. D. Aleksandrov)
53C50	Lorentz流形, 不定度量流形		Lorentz manifolds, manifolds with indefinite metrics
53C55	Hermite和Kähler流形[参见32Cxx]		Hermitian and Kählerian manifolds [See also 32Cxx]
53C56	其它复微分几何[参见32Cxx]		Other complex differential geometry [See also 32Cxx]
53C60	Finsler空间和推广(面积度量)[参见58B20]		Finsler spaces and generalizations (areal metrics) [See also 58B20]
53C65	积分几何[参见52A22, 60D05]; 微分形式、流等[主要见58Axx]		Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]
53C70	直接法(Busemann G-空间等)		Direct methods (G-spaces of Busemann, etc.)
53C75	几何序, 序几何[参见51Lxx]		Geometric orders, order geometry [See also 51Lxx]
53C80	应用于物理		Applications to physics
53C99	其它		None of the above, but in this section
53Dxx	辛几何, 接触几何[参见37Jxx, 70Gxx, 70Hxx]		Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
53D05	辛流形, 一般理论		Symplectic manifolds, general
53D10	接触流形, 一般理论		Contact manifolds, general
53D12	Lagrange子流形; Maslov指数		Lagrangian submanifolds; Maslov index
53D15	殆接触和殆辛流形		Almost contact and almost symplectic manifolds
53D17	Poisson流形; Poisson广群和代数体		Poisson manifolds; Poisson groupoids and algebroids
53D18	广义几何(属于Hitchin)		Generalized geometries (à la Hitchin)
53D20	动量映射; 辛约化		Momentum maps; symplectic reduction
53D22	典型变换		Canonical transformations
53D25	测地流		Geodesic flows
53D30	模空间的辛结构		Symplectic structures of moduli spaces
53D35	辛的整体理论和接触流形[参见57Rxx]		Global theory of symplectic and contact manifolds [See also 57Rxx]
53D37	镜像对称, 辛方面; 同调镜像对称; Fukaya范畴[参见14J33]		Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33]
53D40	Floer(下)同调和上同调, 辛方面		Floer homology and cohomology, symplectic aspects
53D42	辛域论; 接触同调		Symplectic field theory; contact homology
53D45	Gromov-Witten不变量, 量子上同调, Frobenius流形[参见14N35]		Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]
53D50	几何量子化		Geometric quantization
53D55	变形量子化, 星积		Deformation quantization, star products
53D99	其它		None of the above, but in this section
53Zxx	应用于物理		Applications to physics
53Z05	应用于物理		Applications to physics
53Z99	其它		None of the above, but in this section
54-XX	一般拓扑学(所有维流形的拓扑, 见57Nxx)		General topology (For the topology of manifolds of all dimensions, see 57Nxx)
54-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
54-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
54-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
54-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
54-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
54-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
54Axx	一般理论		Generalities
54A05	拓扑空间和推广(闭包空间等)		Topological spaces and generalizations (closure spaces, etc.)
54A10	单集上的多拓扑(拓扑变化, 拓扑比较, 拓扑格)		Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54A15	综合拓扑结构		Syntopogeneous structures
54A20	一般拓扑学的收敛性(序列、滤子、极限、收敛空间等)		Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
54A25	基数性质(基数函数和不等式, 离散子集)[参见03Exx](超滤子, 见54D80)		Cardinality properties (cardinal functions and inequalities, discrete subsets) [See also 03Exx] (For ultrafilters, see 54D80)
54A35	相容性和独立结果[参见03E35]		Consistency and independence results [See also 03E35]
54A40	模糊拓扑[参见03E72]		Fuzzy topology [See also 03E72]
54A99	其它		None of the above, but in this section
54Bxx	基本构造		Basic constructions
54B05	子空间		Subspaces
54B10	积空间		Product spaces
54B15	商空间, 分解		Quotient spaces, decompositions
54B17	附加空间和相似构造		Adjunction spaces and similar constructions
54B20	超空间		Hyperspaces
54B30	范畴方法[参见18B30]		Categorical methods [See also 18B30]
54B35	谱		Spectra
54B40	预层和层[参见18F20]		Presheaves and sheaves [See also 18F20]
54B99	其它		None of the above, but in this section
54Cxx	映射和由映射定义的一般类型空间		Maps and general types of spaces defined by maps
54C05	连续映射		Continuous maps
54C08	弱连续性和广义连续性		Weak and generalized continuity
54C10	拓扑空间的特殊映射(开、闭、完美等)		Special maps on topological spaces (open, closed, perfect, etc.)
54C15	(保核)收缩		Retraction
54C20	映射的扩张		Extension of maps
54C25	嵌入		Embedding
54C30	实值函数[参见26-XX]		Real-valued functions [See also 26-XX]
54C35	函数空间[参见46Exx, 58D15]		Function spaces [See also 46Exx, 58D15]
54C40	函数空间的代数性质[参见46J10]		Algebraic properties of function spaces [See also 46J10]
54C45	C-和C^*-嵌入		C- and C^*-embedding
54C50	由函数定义的特殊集[参见26A21]		Special sets defined by functions [See also 26A21]
54C55	绝对邻域开拓子, 绝对开拓子, 绝对邻域收缩核(ANR), 绝对收缩核空间(一般性质)[参见55M15]		Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) [See also 55M15]
54C56	形状理论[参见55P55, 57N25]		Shape theory [See also 55P55, 57N25]
54C60	集值映射[参见26E25, 28B20, 47H04, 58C06]		Set-valued maps [See also 26E25, 28B20, 47H04, 58C06]
54C65	选择[参见28B20]		Selections [See also 28B20]
54C70	熵		Entropy
54C99	其它		None of the above, but in this section
54Dxx	一般性质		Fairly general properties
54D05	连通和局部连通空间(一般方面)		Connected and locally connected spaces (general aspects)
54D10	下分离公理(T₀-T₃等)		Lower separation axioms (T₀-T₃, etc.)
54D15	高分离公理(完全正则的、正规的、完备或集体式正规的等)		Higher separation axioms (completely regular, normal, perfectly or collection-wise normal, etc.)
54D20	非紧覆盖性质(仿紧性、Lindelöf等)		Noncompact covering properties (paracompact, Lindelöf, etc.)
54D25	“P-极小”和“P-闭”空间		“P-minimal” and “P-closed” spaces
54D30	紧性		Compactness
54D35	空间的扩张(紧化、超紧化、完备化等)		Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54D40	剩余		Remainders
54D45	局部紧性, σ-紧性		Local compactness, σ-compactness
54D50	K-空间		K-spaces
54D55	序列空间		Sequential spaces
54D60	实紧性和实紧化		Realcompactness and realcompactification
54D65	可分性		Separability
54D70	基性质		Base properties
54D80	空间的特殊构造(超滤子空间等)		Special constructions of spaces (spaces of ultrafilters, etc.)
54D99	其它		None of the above, but in this section
54Exx	有较丰富结构的空间		Spaces with richer structures
54E05	邻近结构和推广		Proximity structures and generalizations
54E15	一致结构和推广		Uniform structures and generalizations
54E17	近性空间		Nearness spaces
54E18	p-空间、M-空间、σ-空间等		p-spaces, M-spaces, σ-spaces, etc.
54E20	可层化空间、宇宙空间等		Stratifiable spaces, cosmic spaces, etc.
54E25	半度量空间		Semimetric spaces
54E30	Moore空间		Moore spaces
54E35	度量空间, 可度量性		Metric spaces, metrizability
54E40	度量空间上的特殊映射		Special maps on metric spaces
54E45	紧(局部紧)度量空间		Compact (locally compact) metric spaces
54E50	完备度量空间		Complete metric spaces
54E52	Baire范畴, Baire空间		Baire category, Baire spaces
54E55	双拓扑		Bitopologies
54E70	概率度量空间		Probabilistic metric spaces
54E99	其它		None of the above, but in this section
54Fxx	特殊性质		Special properties
54F05	线性有序拓扑空间, 广义有序空间, 偏序空间[参见06B30, 06F30]		Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30]
54F15	延拓和推广		Continua and generalizations
54F35	高维局部连通性[参见55Mxx, 55Nxx]		Higher-dimensional local connectedness [See also 55Mxx, 55Nxx]
54F45	维数论[参见55M10]		Dimension theory [See also 55M10]
54F50	维数≤1的空间; 曲线, 无圈曲线[参见26A03]		Spaces of dimension ≤1; curves, dendrites [See also 26A03]
54F55	单凝聚, 多凝聚		Unicoherence, multicoherence
54F65	特殊空间的拓扑特征		Topological characterizations of particular spaces
54F99	其它		None of the above, but in this section
54Gxx	独特空间		Peculiar spaces
54G05	极不连通空间、F-空间等		Extremally disconnected spaces, F-spaces, etc.
54G10	P-空间		P-spaces
54G12	散射空间		Scattered spaces
54G15	病态空间		Pathological spaces
54G20	反例		Counterexamples
54G99	其它		None of the above, but in this section
54Hxx	与其它结构的联系, 应用		Connections with other structures, applications
54H05	描述集合论(Borel、解析、投射等集的拓扑方面)[参见03E15, 26A21, 28A05]		Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) [See also 03E15, 26A21, 28A05]
54H10	代数系的拓扑表示[参见22-XX]		Topological representations of algebraic systems [See also 22-XX]
54H11	拓扑群[参见22A05]		Topological groups [See also 22A05]
54H12	拓扑格等[参见06B30, 06F30]		Topological lattices, etc. [See also 06B30, 06F30]
54H13	拓扑域、拓扑环等[参见12Jxx](代数方面, 见13Jxx, 16W80)		Topological fields, rings, etc. [See also 12Jxx] (For algebraic aspects, see 13Jxx, 16W80)
54H15	变换群和半群[参见20M20, 22-XX, 57Sxx]		Transformation groups and semigroups [See also 20M20, 22-XX, 57Sxx]
54H20	拓扑动力学[参见28Dxx, 37Bxx]		Topological dynamics [See also 28Dxx, 37Bxx]
54H25	不动点定理和叠合定理[参见47H10, 55M20]		Fixed-point and coincidence theorems [See also 47H10, 55M20]
54H99	其它		None of the above, but in this section
54Jxx	非标准拓扑[参见03H05]		Nonstandard topology [See also 03H05]
54J05	非标准拓扑[参见03H05]		Nonstandard topology [See also 03H05]
54J99	其它		None of the above, but in this section
55-XX	代数拓扑学		Algebraic topology
55-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
55-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
55-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
55-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
55-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
55-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
55Mxx	经典课题(Euclid空间的拓扑学和流形, 见57Nxx)		Classical topics (For the topology of Euclidean spaces and manifolds, see 57Nxx)
55M05	对偶性		Duality
55M10	维数论[参见54F45]		Dimension theory [See also 54F45]
55M15	绝对邻域收缩核[参见54C55]		Absolute neighborhood retracts [See also 54C55]
55M20	不动点和叠合[参见54H25]		Fixed points and coincidences [See also 54H25]
55M25	度, 分枝数		Degree, winding number
55M30	空间的Ljusternik-Schnirelman (Lyusternik-Shnirelman)范畴		Ljusternik-Schnirelman (Lyusternik-Shnirelman) category of a space
55M35	有限变换群(包括Smith理论)[参见57S17]		Finite groups of transformations (including Smith theory) [See also 57S17]
55M99	其它		None of the above, but in this section
55Nxx	同调和上同调理论[参见57Txx]		Homology and cohomology theories [See also 57Txx]
55N05	Čech型		Čech types
55N07	Steenrod-Sitnikov同调		Steenrod-Sitnikov homologies
55N10	奇异理论		Singular theory
55N15	K-理论[参见19Lxx](代数K-理论, 见18F25, 19-XX)		K-theory [See also 19Lxx] (For algebraic K-theory, see 18F25, 19-XX)
55N20	广义(非常)同调和上同调理论		Generalized (extraordinary) homology and cohomology theories
55N22	加边和配边理论, 形式群定律[参见14L05, 19L41, 57R75, 57R77, 57R85, 57R90]		Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]
55N25	有局部系数的同调, 等变化上同调		Homology with local coefficients, equivariant cohomology
55N30	层上同调[参见18F20, 32C35, 32L10]		Sheaf cohomology [See also 18F20, 32C35, 32L10]
55N32	轨形上同调		Orbifold cohomology
55N33	相交同调和上同调		Intersection homology and cohomology
55N34	椭圆上同调		Elliptic cohomology
55N35	其它同调理论		Other homology theories
55N40	同调论公理和唯一性定理		Axioms for homology theory and uniqueness theorems
55N45	积和交		Products and intersections
55N91	等变化同调和上同调[参见19L47]		Equivariant homology and cohomology [See also 19L47]
55N99	其它		None of the above, but in this section
55Pxx	同伦理论(简单同伦型, 见57Q10)		Homotopy theory (For simple homotopy type, see 57Q10)
55P05	同伦扩张性质, 上纤维化		Homotopy extension properties, cofibrations
55P10	同伦等价		Homotopy equivalences
55P15	同伦型的分类		Classification of homotopy type
55P20	Eilenberg-Mac Lane空间		Eilenberg-Mac Lane spaces
55P25	Spanier-Whitehead对偶性		Spanier-Whitehead duality
55P30	Eckmann-Hilton对偶性		Eckmann-Hilton duality
55P35	圈空间		Loop spaces
55P40	同纬映射		Suspensions
55P42	稳定同伦理论, 谱		Stable homotopy theory, spectra
55P43	具有附加结构的谱(E_∞、A_∞、环谱等)		Spectra with additional structure (E_∞, A_∞, ring spectra, etc.)
55P45	H-空间和对偶		H-spaces and duals
55P47	无限圈空间		Infinite loop spaces
55P48	圈空间机器, operads[参见18D50]		Loop space machines, operads [See also 18D50]
55P50	String拓扑		String topology
55P55	形状理论[参见54C56, 55Q07]		Shape theory [See also 54C56, 55Q07]
55P57	真同伦理论		Proper homotopy theory
55P60	局部化和完备化		Localization and completion
55P62	有理同伦理论		Rational homotopy theory
55P65	同伦函子		Homotopy functors
55P91	等变化同伦理论[参见19L47]		Equivariant homotopy theory [See also 19L47]
55P92	等变同伦论与非等变同伦论之间的关系		Relations between equivariant and nonequivariant homotopy theory
55P99	其它		None of the above, but in this section
55Qxx	同伦群		Homotopy groups
55Q05	同伦群, 一般理论; 同伦类集合		Homotopy groups, general; sets of homotopy classes
55Q07	形状群		Shape groups
55Q10	稳定同伦群		Stable homotopy groups
55Q15	Whitehead积和推广		Whitehead products and generalizations
55Q20	楔, 联和单空间同伦群		Homotopy groups of wedges, joins, and simple spaces
55Q25	Hopf不变量		Hopf invariants
55Q35	同伦群运算		Operations in homotopy groups
55Q40	球同伦群		Homotopy groups of spheres
55Q45	稳定球同伦		Stable homotopy of spheres
55Q50	J-射[参见19L20]		J-morphism [See also 19L20]
55Q51	V_n周期性		V_n-periodicity
55Q52	特殊空间的同伦群		Homotopy groups of special spaces
55Q55	上同伦群		Cohomotopy groups
55Q70	特殊型同伦群[参见55N05, 55N07]		Homotopy groups of special types [See also 55N05, 55N07]
55Q91	等变化同伦群[参见19L47]		Equivariant homotopy groups [See also 19L47]
55Q99	其它		None of the above, but in this section
55Rxx	纤维空间和纤维丛[参见18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]		Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]
55R05	纤维空间		Fiber spaces
55R10	纤维丛		Fiber bundles
55R12	转移		Transfer
55R15	分类		Classification
55R20	纤维空间的谱序列和同调[参见55Txx]		Spectral sequences and homology of fiber spaces [See also 55Txx]
55R25	球丛和向量丛		Sphere bundles and vector bundles
55R35	群的分类空间和H-空间		Classifying spaces of groups and H-spaces
55R37	分类空间之间的映射		Maps between classifying spaces
55R40	分类空间的同调, 特征类[参见57Txx, 57R20]		Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
55R45	BO, BU的同调和同伦; Bott周期性		Homology and homotopy of BO, and BU; Bott periodicity
55R50	向量空间丛的稳定类, K-理论[参见19Lxx](代数K-理论, 见18F25, 19-XX)		Stable classes of vector space bundles, K-theory [See also 19Lxx] (For algebraic K-theory, see 18F25, 19-XX)
55R55	具有奇异性的纤维化		Fiberings with singularities
55R60	微丛和块丛[参见57N55, 57Q50]		Microbundles and block bundles [See also 57N55, 57Q50]
55R65	纤维空间和纤维丛的推广		Generalizations of fiber spaces and bundles
55R70	纤维式拓扑		Fibrewise topology
55R80	判别式簇, 构形空间		Discriminantal varieties, configuration spaces
55R91	等变化的纤维空间和纤维丛[参见19L47]		Equivariant fiber spaces and bundles [See also 19L47]
55R99	其它		None of the above, but in this section
55Sxx	运算和障碍		Operations and obstructions
55S05	一阶上同调运算		Primary cohomology operations
55S10	Steenrod代数		Steenrod algebra
55S12	Dyer-Lashof运算		Dyer-Lashof operations
55S15	对称积, 循环积		Symmetric products, cyclic products
55S20	二阶和高阶上同调运算		Secondary and higher cohomology operations
55S25	K-理论运算和广义上同调运算[参见19D55, 19Lxx]		K-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
55S30	Massey积		Massey products
55S35	障碍理论		Obstruction theory
55S36	映射的扩张和压缩		Extension and compression of mappings
55S37	映射的分类		Classification of mappings
55S40	分割纤维空间和纤维丛		Sectioning fiber spaces and bundles
55S45	Postnikov系统, k-不变式		Postnikov systems, k-invariants
55S91	等变化运算和障碍[参见19L47]		Equivariant operations and obstructions [See also 19L47]
55S99	其它		None of the above, but in this section
55Txx	谱序列[参见18G40, 55R20]		Spectral sequences [See also 18G40, 55R20]
55T05	一般理论		General
55T10	Serre谱序列		Serre spectral sequences
55T15	Adams谱序列		Adams spectral sequences
55T20	Eilenberg-Moore谱序列[参见57T35]		Eilenberg-Moore spectral sequences [See also 57T35]
55T25	广义上同调		Generalized cohomology
55T99	其它		None of the above, but in this section
55Uxx	应用同调代数和范畴论[参见18Gxx]		Applied homological algebra and category theory [See also 18Gxx]
55U05	抽象复形		Abstract complexes
55U10	单纯集和复形		Simplicial sets and complexes
55U15	链复形		Chain complexes
55U20	万有系数定理, Bockstein算子		Universal coefficient theorems, Bockstein operator
55U25	积的同调, Künneth公式		Homology of a product, Künneth formula
55U30	对偶性		Duality
55U35	抽象和公理同伦理论		Abstract and axiomatic homotopy theory
55U40	拓扑范畴, 同伦论的基础		Topological categories, foundations of homotopy theory
55U99	其它		None of the above, but in this section
57-XX	流形和胞腔复形(复流形, 见32Qxx)		Manifolds and cell complexes (For complex manifolds, see 32Qxx)
57-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
57-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
57-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
57-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
57-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
57-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
57Mxx	低维拓扑		Low-dimensional topology
57M05	基本群, 表示, 自由微分演算		Fundamental group, presentations, free differential calculus
57M07	群论中的拓扑方法		Topological methods in group theory
57M10	覆盖空间		Covering spaces
57M12	特殊覆盖, 例如: 分枝覆盖		Special coverings, e.g. branched
57M15	与图论的关系[参见05Cxx]		Relations with graph theory [See also 05Cxx]
57M20	二维复形		Two-dimensional complexes
57M25	S³中的纽结和连接(高维, 见57Q45)		Knots and links in S³ (For higher dimensions, see 57Q45)
57M27	纽结不变量和三维流形		Invariants of knots and 3-manifolds
57M30	病态纽结和曲面等, 病态嵌入		Wild knots and surfaces, etc., wild embeddings
57M35	Dehn引理, 球面定理, 圈定理, 非球面性		Dehn’s lemma, sphere theorem, loop theorem, asphericity
57M40	E³和S³的特征(Poincaré猜想)[参见57N12]		Characterizations of E³ and S³ (Poincaré conjecture) [See also 57N12]
57M50	低维流形的几何结构		Geometric structures on low-dimensional manifolds
57M60	低维中的群作用		Group actions in low dimensions
57M99	其它		None of the above, but in this section
57Nxx	拓扑流形		Topological manifolds
57N05	E²的拓扑, 2维流形		Topology of E², 2-manifolds
57N10	一般3维流形的拓扑[参见57Mxx]		Topology of general 3-manifolds [See also 57Mxx]
57N12	E³和S³的拓扑[参见57M40]		Topology of E³ and S³ [See also 57M40]
57N13	E⁴的拓扑, 4维流形[参见14Jxx, 32Jxx]		Topology of E⁴, 4-manifolds [See also 14Jxx, 32Jxx]
57N15	Eⁿ的拓扑, n-维流形(4<n<∞)		Topology of Eⁿ, n-manifolds (4<n<∞)
57N16	流形上的几何结构[参见57M50]		Geometric structures on manifolds [See also 57M50]
57N17	拓扑向量空间的拓扑学		Topology of topological vector spaces
57N20	无限维流形的拓扑学[参见58Bxx]		Topology of infinite-dimensional manifolds [See also 58Bxx]
57N25	形状[参见54C56, 55P55, 55Q07]		Shapes [See also 54C56, 55P55, 55Q07]
57N30	淹没		Engulfing
57N35	嵌入和浸入		Embeddings and immersions
57N37	合痕和伪合痕		Isotopy and pseudo-isotopy
57N40	子流形的邻域		Neighborhoods of submanifolds
57N45	平坦性和驯顺性		Flatness and tameness
57N50	Sⁿ^-1⊂Eⁿ, Schoenflies问题		Sⁿ^-1⊂Eⁿ, Schoenflies problem
57N55	微丛和块丛[参见55R60, 57Q50]		Microbundles and block bundles [See also 55R60, 57Q50]
57N60	胞腔性		Cellularity
57N65	流形的代数拓扑		Algebraic topology of manifolds
57N70	配边与和谐性		Cobordism and concordance
57N75	一般位置和横截性		General position and transversality
57N80	层次		Stratifications
57N99	其它		None of the above, but in this section
57Pxx	广义流形[参见18F15]		Generalized manifolds [See also 18F15]
57P05	广义流形的局部性质		Local properties of generalized manifolds
57P10	Poincaré对偶性空间		Poincaré duality spaces
57P99	其它		None of the above, but in this section
57Qxx	PL-拓扑		PL-topology
57Q05	复形的一般拓扑		General topology of complexes
57Q10	单同调型、Whitehead挠率、Reidemeister-Franz挠率等[参见19B28]		Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28]
57Q12	CW复形的Wall有限性障碍		Wall finiteness obstruction for CW-complexes
57Q15	三角剖分化流形		Triangulating manifolds
57Q20	配边		Cobordism
57Q25	PL结构的比较: 分类, Hauptvermutung主要猜想		Comparison of PL-structures: classification, Hauptvermutung
57Q30	淹没		Engulfing
57Q35	嵌入和浸入		Embeddings and immersions
57Q37	合痕		Isotopy
57Q40	正则邻域		Regular neighborhoods
57Q45	(高维中)纽结和连接(低维情形, 见57M25)		Knots and links (in high dimensions) (For the low-dimensional case, see 57M25)
57Q50	微丛和块丛[参见55R60, 57N55]		Microbundles and block bundles [See also 55R60, 57N55]
57Q55	逼近		Approximations
57Q60	配边与和谐性		Cobordism and concordance
57Q65	一般位置和横截性		General position and transversality
57Q91	等变化的PL-拓扑		Equivariant PL-topology
57Q99	其它		None of the above, but in this section
57Rxx	微分拓扑(可微流形的基本问题, 见58Axx; 无限维流形, 见58Bxx)		Differential topology (For foundational questions of differentiable manifolds, see 58Axx; for infinite-dimensional manifolds, see 58Bxx)
57R05	三角剖分		Triangulating
57R10	光滑性		Smoothing
57R12	光滑逼近		Smooth approximations
57R15	流形上的特定化结构(旋量流形、标架流形等)		Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57R17	辛拓扑和接触拓扑		Symplectic and contact topology
57R18	轨形拓扑和几何		Topology and geometry of orbifolds
57R19	流形上的代数拓扑		Algebraic topology on manifolds
57R20	示性类和示性数		Characteristic classes and numbers
57R22	向量丛拓扑和纤维丛拓扑[参见55Rxx]		Topology of vector bundles and fiber bundles [See also 55Rxx]
57R25	向量场, 标架场		Vector fields, frame fields
57R27	C^∞和实解析流形上的向量场的可控性[参见49Qxx, 37C10, 93B05]		Controllability of vector fields on C^∞ and real-analytic manifolds [See also 49Qxx, 37C10, 93B05]
57R30	叶状结构物; 几何理论		Foliations; geometric theory
57R32	叶状结构物的分类空间; Gelfand-Fuks上同调[参见58H10]		Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10]
57R35	可微映射		Differentiable mappings
57R40	嵌入		Embeddings
57R42	浸入		Immersions
57R45	可微映射的奇异性		Singularities of differentiable mappings
57R50	微分同胚		Diffeomorphisms
57R52	合痕		Isotopy
57R55	可微结构		Differentiable structures
57R56	拓扑量子场论		Topological quantum field theories
57R57	整体分析在流形、Donaldson和Seiberg-Witten不变量结构中的应用[参见58-XX]		Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]
57R58	Floer(下)同调		Floer homology
57R60	同伦球面, Poincaré猜想		Homotopy spheres, Poincaré conjecture
57R65	换球术和环柄体		Surgery and handlebodies
57R67	换球术障碍, Wall群[参见19J25]		Surgery obstructions, Wall groups [See also 19J25]
57R70	临界点和临界子流形		Critical points and critical submanifolds
57R75	O配边和SO配边		O- and SO-cobordism
57R77	复配边(U-配边和SU-配边)[参见55N22]		Complex cobordism (U- and SU-cobordism) [See also 55N22]
57R80	h-配边和s-配边		h- and s-cobordism
57R85	等变化配边		Equivariant cobordism
57R90	其它类型配边[参见55N22]		Other types of cobordism [See also 55N22]
57R91	流形的等变代数拓扑		Equivariant algebraic topology of manifolds
57R95	由子流形实现的循环		Realizing cycles by submanifolds
57R99	其它		None of the above, but in this section
57Sxx	拓扑变换群[参见20F34, 22-XX, 37-XX, 54H15, 58D05]		Topological transformation groups [See also 20F34, 22-XX, 37-XX, 54H15, 58D05]
57S05	同胚或微分同胚群的拓扑性质		Topological properties of groups of homeomorphisms or diffeomorphisms
57S10	同胚的紧群		Compact groups of homeomorphisms
57S15	可微变换的紧Lie群		Compact Lie groups of differentiable transformations
57S17	有限变换群		Finite transformation groups
57S20	变换非紧Lie群		Noncompact Lie groups of transformations
57S25	作用在特殊流形上的群		Groups acting on specific manifolds
57S30	变换的不连续群		Discontinuous groups of transformations
57S99	其它		None of the above, but in this section
57Txx	拓扑群及相关结构的同调和同伦		Homology and homotopy of topological groups and related structures
57T05	Hopf代数[参见16T05]		Hopf algebras [See also 16T05]
57T10	Lie群的同调和上同调		Homology and cohomology of Lie groups
57T15	Lie群齐次空间的同调和上同调		Homology and cohomology of homogeneous spaces of Lie groups
57T20	拓扑群和齐次空间的同伦群		Homotopy groups of topological groups and homogeneous spaces
57T25	H-空间的同调和上同调		Homology and cohomology of H-spaces
57T30	带和同带构造[参见18G55, 55Uxx]		Bar and cobar constructions [See also 18G55, 55Uxx]
57T35	Eilenberg-Moore谱序列的应用[参见55R20, 55T20]		Applications of Eilenberg-Moore spectral sequences [See also 55R20, 55T20]
57T99	其它		None of the above, but in this section
58-XX	大范围分析, 流形上的分析[参见32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](几何积分理论, 见49Q15)		Global analysis, analysis on manifolds [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx] (For geometric integration theory, see 49Q15)
58-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
58-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
58-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
58-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
58-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
58-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
58Axx	可微流形的一般理论[参见32Cxx]		General theory of differentiable manifolds [See also 32Cxx]
58A03	Topos理论近似可微流形		Topos-theoretic approach to differentiable manifolds
58A05	可微流形, 基础		Differentiable manifolds, foundations
58A07	实解析流形和Nash流形[参见14P20, 32C07]		Real-analytic and Nash manifolds [See also 14P20, 32C07]
58A10	微分形式		Differential forms
58A12	de Rham理论[参见14Fxx]		de Rham theory [See also 14Fxx]
58A14	Hodge理论[参见14C30, 14Fxx, 32J25, 32S35]		Hodge theory [See also 14C30, 14Fxx, 32J25, 32S35]
58A15	外微分系统(Cartan理论)		Exterior differential systems (Cartan theory)
58A17	Pfaff系统		Pfaffian systems
58A20	射流		Jets
58A25	流[参见32C30, 53C65]		Currents [See also 32C30, 53C65]
58A30	向量分布(切丛的子丛)		Vector distributions (subbundles of the tangent bundles)
58A32	自然丛		Natural bundles
58A35	分层集[参见32S60]		Stratified sets [See also 32S60]
58A40	微分空间		Differential spaces
58A50	超流形和分次流形[参见14A22, 32C11]		Supermanifolds and graded manifolds [See also 14A22, 32C11]
58A99	其它		None of the above, but in this section
58Bxx	无限维流形		Infinite-dimensional manifolds
58B05	同伦和拓扑问题		Homotopy and topological questions
58B10	可微性问题		Differentiability questions
58B12	全纯问题[参见32-XX, 46G20]		Questions of holomorphy [See also 32-XX, 46G20]
58B15	Fredholm结构[参见47A53]		Fredholm structures [See also 47A53]
58B20	Riemann, Finsler, 和其它几何结构[参见53C20, 53C60]		Riemannian, Finsler and other geometric structures [See also 53C20, 53C60]
58B25	无限维流形上的群结构和推广[参见22E65, 58D05]		Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]
58B32	量子群的几何		Geometry of quantum groups
58B34	非交换几何(属于Connes)		Noncommutative geometry (à la Connes)
58B99	其它		None of the above, but in this section
58Cxx	流形上的微积分; 非线性算子[参见46Txx, 47Hxx, 47Jxx]		Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx]
58C05	实值函数		Real-valued functions
58C06	集值映射和函数空间值映射[参见47H04, 54C60]		Set valued and function-space valued mappings [See also 47H04, 54C60]
58C07	映射的连续性性质		Continuity properties of mappings
58C10	全纯映射[参见32-XX]		Holomorphic maps [See also 32-XX]
58C15	隐函数定理; 整体Newton法		Implicit function theorems; global Newton methods
58C20	微分法理论(Gateaux、Fréchet等)[参见26Exx, 46G05]		Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]
58C25	可微映射		Differentiable maps
58C30	流形上的不动点定理[参见47H10]		Fixed point theorems on manifolds [See also 47H10]
58C35	流形上的积分法; 流形上的测度[参见28Cxx]		Integration on manifolds; measures on manifolds [See also 28Cxx]
58C40	谱理论; 特征值问题[参见47J10, 58E07]		Spectral theory; eigenvalue problems [See also 47J10, 58E07]
58C50	超流形或分次流形上的分析		Analysis on supermanifolds or graded manifolds
58C99	其它		None of the above, but in this section
58Dxx	映射的空间和流形(包括46Exx的非线性形式)[参见46Txx, 53Cxx]		Spaces and manifolds of mappings (including nonlinear versions of 46Exx) [See also 46Txx, 53Cxx]
58D05	微分同胚群和作为流形的自同胚群[参见22E65, 57S05]		Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
58D07	非线性算子的群和半群[参见17B65, 47H20]		Groups and semigroups of nonlinear operators [See also 17B65, 47H20]
58D10	嵌入和浸入的空间		Spaces of imbeddings and immersions
58D15	映射流形[参见46T10, 54C35]		Manifolds of mappings [See also 46T10, 54C35]
58D17	度量流形(特别是Riemann)		Manifolds of metrics (esp. Riemannian)
58D19	群的作用和对称性质		Group actions and symmetry properties
58D20	映射流形上的测度(Gauss的、圆柱形的等)[参见28Cxx, 46T12]		Measures (Gaussian, cylindrical, etc.) on manifolds of maps [See also 28Cxx, 46T12]
58D25	函数空间中的方程; 发展方程[参见34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]		Equations in function spaces; evolution equations [See also 34Gxx, 35K90, 35L90, 35R15, 37Lxx, 47Jxx]
58D27	微分几何结构的模问题		Moduli problems for differential geometric structures
58D29	拓扑结构的模问题		Moduli problems for topological structures
58D30	应用(在量子力学(Feynman路径积分)、相对性、流体动力学等)		Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)
58D99	其它		None of the above, but in this section
58Exx	无限维空间中的变分问题		Variational problems in infinite-dimensional spaces
58E05	抽象临界点理论(Morse理论、Ljusternik-Schnirelman (Lyusternik-Shnirelman)理论等)		Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirelman) theory, etc.)
58E07	抽象分歧理论		Abstract bifurcation theory
58E09	群不变分歧理论		Group-invariant bifurcation theory
58E10	应用于测地线的理论(单独立变量问题)		Applications to the theory of geodesics (problems in one independent variable)
58E11	临界度量		Critical metrics
58E12	应用于极小曲面(双独立变量问题)[参见49Q05]		Applications to minimal surfaces (problems in two independent variables) [See also 49Q05]
58E15	应用于多变量极值问题; Yang-Mills泛函[参见81T13]等		Application to extremal problems in several variables; Yang-Mills functionals [See also 81T13], etc.
58E17	Pareto最优性等, 经济学中的应用[参见90C29]		Pareto optimality, etc., applications to economics [See also 90C29]
58E20	调和映射[参见53C43]等		Harmonic maps [See also 53C43], etc.
58E25	控制论中的应用[参见49-XX, 93-XX]		Applications to control theory [See also 49-XX, 93-XX]
58E30	变分原理		Variational principles
58E35	变分不等式(整体问题)		Variational inequalities (global problems)
58E40	群的作用		Group actions
58E50	应用		Applications
58E99	其它		None of the above, but in this section
58Hxx	流形上的伪群, 可微广群和一般结构	Pseudogroups, differentiable groupoids and general structures on manifolds
58H05	伪群和可微广群[参见22A22, 22E65]		Pseudogroups and differentiable groupoids [See also 22A22, 22E65]
58H10	伪群结构(Spencer、Gelfand-Fuks等)分类空间的上同调[参见57R32]		Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]
58H15	结构的形变[参见32Gxx, 58J10]		Deformations of structures [See also 32Gxx, 58J10]
58H99	其它		None of the above, but in this section
58Jxx	流形上的偏微分方程; 微分算子[参见32Wxx, 35-XX, 53Cxx]		Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx]
58J05	流形上的椭圆型方程, 一般理论[参见35-XX]		Elliptic equations on manifolds, general theory [See also 35-XX]
58J10	微分复形[参见35Nxx]; 椭圆复形		Differential complexes [See also 35Nxx]; elliptic complexes
58J15	与超函数的关系		Relations with hyperfunctions
58J20	指数理论及相关的不动点定理[参见19K56, 46L80]		Index theory and related fixed point theorems [See also 19K56, 46L80]
58J22	异种指数理论[参见19K56, 46L05, 46L10, 46L80, 46M20]		Exotic index theories [See also 19K56, 46L05, 46L10, 46L80, 46M20]
58J26	椭圆亏格		Elliptic genera
58J28	Eta-不变量, Chern-Simons不变量		Eta-invariants, Chern-Simons invariants
58J30	谱流		Spectral flows
58J32	流形上的边值问题		Boundary value problems on manifolds
58J35	热和其它抛物型方程方法		Heat and other parabolic equation methods
58J37	摄动; 渐近性		Perturbations; asymptotics
58J40	流形上的伪微分和Fourier积分算子[参见35Sxx]		Pseudodifferential and Fourier integral operators on manifolds [See also 35Sxx]
58J42	非交换整体分析, 非交换剩余		Noncommutative global analysis, noncommutative residues
58J45	双曲型方程[参见35Lxx]		Hyperbolic equations [See also 35Lxx]
58J47	奇异性传播; 初值问题		Propagation of singularities; initial value problems
58J50	谱问题; 谱几何; 散射理论[参见35Pxx]		Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
58J51	谱理论和遍历理论之间的关系, 例如: 量子唯一遍历性		Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
58J52	行列式和行列式丛, 解析挠率		Determinants and determinant bundles, analytic torsion
58J53	等谱性		Isospectrality
58J55	分歧[参见35B32]		Bifurcation [See also 35B32]
58J60	与特殊流形结构的关系(Riemann、Finsler等)		Relations with special manifold structures (Riemannian, Finsler, etc.)
58J65	流形上的扩散过程和随机分析[参见35R60, 60H10, 60J60]		Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
58J70	不变性和对称性质[参见35A30]		Invariance and symmetry properties [See also 35A30]
58J72	对应和其它变换方法(例如: Lie-Bäcklund)[参见35A22]		Correspondences and other transformation methods (e.g. Lie-Bäcklund) [See also 35A22]
58J90	应用		Applications
58J99	其它		None of the above, but in this section
58Kxx	奇异性理论和突变理论[参见32Sxx, 37-XX]		Theory of singularities and catastrophe theory [See also 32Sxx, 37-XX]
58K05	函数和映射的临界点		Critical points of functions and mappings
58K10	单值[性]		Monodromy
58K15	映射的拓扑性质		Topological properties of mappings
58K20	映射的代数和解析性质		Algebraic and analytic properties of mappings
58K25	稳定性		Stability
58K30	全局理论		Global theory
58K35	突变理论		Catastrophe theory
58K40	分类; 映射芽的有限确定性		Classification; finite determinacy of map germs
58K45	向量场的奇异性, 拓扑方面		Singularities of vector fields, topological aspects
58K50	标准型		Normal forms
58K55	渐近性态		Asymptotic behavior
58K60	奇异性的变形		Deformation of singularities
58K65	拓扑不变量		Topological invariants
58K70	对称性, 同变性		Symmetries, equivariance
58K99	其它		None of the above, but in this section
58Zxx	在物理上的应用		Applications to physics
58Z05	在物理上的应用		Applications to physics
58Z99	其它		None of the above, but in this section
60-XX	概率论和随机过程(其它应用, 见11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)		Probability theory and stochastic processes (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)
60-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
60-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
60-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
60-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
60-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
60-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
60-08	计算方法(在更特殊等级上不分类)[参见65C50]		Computational methods (not classified at a more specific level) [See also 65C50]
60Axx	概率论基础		Foundations of probability theory
60A05	公理; 其它一般问题		Axioms; other general questions
60A10	概率测度论(遍历理论, 见28Dxx和60Fxx)		Probabilistic measure theory (For ergodic theory, see 28Dxx and 60Fxx)
60A86	模糊概率		Fuzzy probability
60A99	其它		None of the above, but in this section
60Bxx	代数结构和拓扑结构上的概率论		Probability theory on algebraic and topological structures
60B05	拓扑空间上的概率测度		Probability measures on topological spaces
60B10	概率测度的收敛性		Convergence of probability measures
60B11	线性拓扑空间上的概率理论[参见28C20]		Probability theory on linear topological spaces [See also 28C20]
60B12	向量值随机变量的极限定理(无限维情形)		Limit theorems for vector-valued random variables (infinite-dimensional case)
60B15	群或半群、Fourier变换、因子分解上的概率测度		Probability measures on groups or semigroups, Fourier transforms, factorization
60B20	随机矩阵(概率方面; 代数方面见15B52)		Random matrices (probabilistic aspects; for algebraic aspects see 15B52)
60B99	其它		None of the above, but in this section
60Cxx	组合概率		Combinatorial probability
60C05	组合概率		Combinatorial probability
60C99	其它		None of the above, but in this section
60Dxx	几何概率和随机几何[参见52A22, 53C65]		Geometric probability and stochastic geometry [See also 52A22, 53C65]
60D05	几何概率和随机几何[参见52A22, 53C65]		Geometric probability and stochastic geometry [See also 52A22, 53C65]
60D99	其它		None of the above, but in this section
60Exx	分布论[参见62Exx, 62Hxx]		Distribution theory [See also 62Exx, 62Hxx]
60E05	分布: 一般理论		Distributions: general theory
60E07	无限可分分布; 稳定分布		Infinitely divisible distributions; stable distributions
60E10	特征函数; 其它变换		Characteristic functions; other transforms
60E15	不等式; 随机序		Inequalities; stochastic orderings
60E99	其它		None of the above, but in this section
60Fxx	极限定理[参见28Dxx, 60B12]		Limit theorems [See also 28Dxx, 60B12]
60F05	中心极限定理和其它弱定理		Central limit and other weak theorems
60F10	大偏差		Large deviations
60F15	强定理		Strong theorems
60F17	泛函极限定理; 不变性原理		Functional limit theorems; invariance principles
60F20	0-1定律		Zero-one laws
60F25	L^p-极限定理		L^p-limit theorems
60F99	其它		None of the above, but in this section
60Gxx	随机过程		Stochastic processes
60G05	随机过程的基础		Foundations of stochastic processes
60G07	过程的一般理论		General theory of processes
60G09	可交换性		Exchangeability
60G10	平稳过程		Stationary processes
60G12	一般二阶过程		General second-order processes
60G15	Gauss过程		Gaussian processes
60G17	样本道路性质		Sample path properties
60G18	自相似过程		Self-similar processes
60G20	广义随机过程		Generalized stochastic processes
60G22	分式过程, 包括分式Brown运动		Fractional processes, including fractional Brownian motion
60G25	预报理论[参见62M20]		Prediction theory [See also 62M20]
60G30	诱导测度的连续性和奇异性		Continuity and singularity of induced measures
60G35	信号检测和滤波[参见62M20, 93E10, 93E11, 94Axx]		Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]
60G40	停止时间; 最优停止问题; 博弈论[参见62L15, 91A60]		Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
60G42	离散参数的鞅		Martingales with discrete parameter
60G44	连续参数的鞅		Martingales with continuous parameter
60G46	鞅和经典分析		Martingales and classical analysis
60G48	鞅的推广		Generalizations of martingales
60G50	独立随机变量的和; 随机游动		Sums of independent random variables; random walks
60G51	独立增量过程; Lévy过程		Processes with independent increments; Lévy processes
60G52	稳定过程		Stable processes
60G55	点过程		Point processes
60G57	随机测度		Random measures
60G60	随机场		Random fields
60G70	极值理论; 极值过程		Extreme value theory; extremal processes
60G99	其它		None of the above, but in this section
60Hxx	随机分析[参见58J65]		Stochastic analysis [See also 58J65]
60H05	随机积分		Stochastic integrals
60H07	变分随机微积分和Malliavin微积分		Stochastic calculus of variations and the Malliavin calculus
60H10	随机常微分方程[参见34F05]		Stochastic ordinary differential equations [See also 34F05]
60H15	随机偏微分方程[参见35R60]		Stochastic partial differential equations [See also 35R60]
60H20	随机积分方程		Stochastic integral equations
60H25	随机算子和方程[参见47B80]		Random operators and equations [See also 47B80]
60H30	随机分析的应用(偏微分方程等)		Applications of stochastic analysis (to PDE, etc.)
60H35	随机方程的计算方法[参见65C30]		Computational methods for stochastic equations [See also 65C30]
60H40	白噪声理论		White noise theory
60H99	其它		None of the above, but in this section
60Jxx	Markov过程		Markov processes
60J05	一般状态空间上离散时间Markov过程		Discrete-time Markov processes on general state spaces
60J10	Markov链(离散状态空间上离散时间Markov过程)		Markov chains (discrete-time Markov processes on discrete state spaces)
60J20	一般状态空间上Markov链和离散时间Markov过程的应用(社会迁移率、学习理论、工业过程等)[参见90B30, 91D10, 91D35, 91E40]		Applications of Markov chains and discrete-time Markov processes on general state spaces(social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
60J22	Markov链中的计算方法[参见65C40]		Computational methods in Markov chains [See also 65C40]
60J25	一般状态空间上连续时间Markov过程		Continuous-time Markov processes on general state spaces
60J27	离散状态空间上连续时间Markov过程		Continuous-time Markov processes on discrete state spaces
60J28	离散状态空间上连续时间Markov过程的应用		Applications of continuous-time Markov processes on discrete state spaces
60J35	转移函数, 生成元和预解式[参见47D03, 47D07]		Transition functions, generators and resolvents [See also 47D03, 47D07]
60J40	右过程		Right processes
60J45	概率位势论[参见31Cxx, 31D05]		Probabilistic potential theory [See also 31Cxx, 31D05]
60J50	边界理论		Boundary theory
60J55	局部时间和加性泛函		Local time and additive functionals
60J57	乘性泛函		Multiplicative functionals
60J60	扩散过程[参见58J65]		Diffusion processes [See also 58J65]
60J65	Brown运动[参见58J65]		Brownian motion [See also 58J65]
60J67	随机(Schramm-)Loewner进化(SLE)		Stochastic (Schramm-）Loewner evolution (SLE)
60J68	超过程		Superprocesses
60J70	Brown运动和扩散理论的应用(人口遗传学、吸收问题等)[参见92Dxx]		Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
60J75	跳跃过程		Jump processes
60J80	分枝过程(Galton-Waston过程、生灭过程等)		Branching processes (Galton-Watson, birth-and-death, etc.)
60J85	分枝过程的应用[参见92Dxx]		Applications of branching processes [See also 92Dxx]
60J99	其它		None of the above, but in this section
60Kxx	特殊过程		Special processes
60K05	更新理论		Renewal theory
60K10	应用(可靠性、需求理论等)		Applications (reliability, demand theory, etc.)
60K15	Markov更新过程, 半Markov过程		Markov renewal processes, semi-Markov processes
60K20	Markov更新过程的应用(可靠性、排队网络等)[参见90Bxx]		Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]
60K25	排队论[参见68M20, 90B22]		Queueing theory [See also 68M20, 90B22]
60K30	应用(密集、配置、存贮、交通等)[参见90Bxx]		Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
60K35	交互作用随机过程; 统计力学型模型; 渗透理论[参见82B43, 82C43]		Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
60K37	随机环境中的过程		Processes in random environments
60K40	随机过程的其它物理应用		Other physical applications of random processes
60K99	其它		None of the above, but in this section
62-XX	统计学		Statistics
62-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
62-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
62-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
62-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
62-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
62-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
62-07	数据分析		Data analysis
62-09	图解法		Graphical methods
62Axx	基础和哲学论题		Foundational and philosophical topics
62A01	基础和哲学论题		Foundational and philosophical topics
62A86	统计学中的模糊分析		Fuzzy analysis in statistics
62A99	其它		None of the above, but in this section
62Bxx	充分性和信息		Sufficiency and information
62B05	充分统计学和域		Sufficient statistics and fields
62B10	信息论课题[参见94A17]		Information-theoretic topics [See also 94A17]
62B15	统计实验的理论		Theory of statistical experiments
62B86	模糊性, 充分性和信息		Fuzziness, sufficiency, and information
62B99	其它		None of the above, but in this section
62Cxx	决策理论[参见90B50, 91B06](对策论, 见91A35)		Decision theory [See also 90B50, 91B06] (For game theory, see 91A35)
62C05	一般考虑		General considerations
62C07	完全类结果		Complete class results
62C10	Bayes问题; Bayes方法的特性		Bayesian problems; characterization of Bayes procedures
62C12	经验决策方法; 经验Bayes方法		Empirical decision procedures; empirical Bayes procedures
62C15	容许性		Admissibility
62C20	极大极小方法		Minimax procedures
62C25	复合决策问题		Compound decision problems
62C86	决策论与模糊性		Decision theory and fuzziness
62C99	其它		None of the above, but in this section
62Dxx	抽样理论, 样本调查		Sampling theory, sample surveys
62D05	抽样理论, 样本调查		Sampling theory, sample surveys
62D99	其它		None of the above, but in this section
62Exx	分布论[参见60Exx]		Distribution theory [See also 60Exx]
62E10	特征和结构理论		Characterization and structure theory
62E15	精确分布论		Exact distribution theory
62E17	分布近似(非渐近)		Approximations to distributions (nonasymptotic)
62E20	渐近分布论		Asymptotic distribution theory
62E86	本节中与分布主题相关的模糊性		Fuzziness in connection with the topics on distributions in this section
62E99	其它		None of the above, but in this section
62Fxx	参数推断		Parametric inference
62F03	假设检验		Hypothesis testing
62F05	检验的渐近性质		Asymptotic properties of tests
62F07	秩评定和选择		Ranking and selection
62F10	点估计		Point estimation
62F12	估计量的渐近性质		Asymptotic properties of estimators
62F15	Bayes推断		Bayesian inference
62F25	容许区域和置信区域		Tolerance and confidence regions
62F30	约束下的推断		Inference under constraints
62F35	稳健性和自适应过程		Robustness and adaptive procedures
62F40	自助法、刀切法和其它再抽样法		Bootstrap, jackknife and other resampling methods
62F86	参数推断和模糊性		Parametric inference and fuzziness
62F99	其它		None of the above, but in this section
62Gxx	非参数推断		Nonparametric inference
62G05	估计		Estimation
62G07	密度估计		Density estimation
62G08	非参数回归		Nonparametric regression
62G09	再抽样法		Resampling methods
62G10	假设检验		Hypothesis testing
62G15	容许区域和置信区域		Tolerance and confidence regions
62G20	渐近性质		Asymptotic properties
62G30	顺序统计学; 经验分布函数		Order statistics; empirical distribution functions
62G32	极值统计学; 尾推论		Statistics of extreme values; tail inference
62G35	稳健性		Robustness
62G86	非参数推断和模糊性		Nonparametric inference and fuzziness
62G99	其它		None of the above, but in this section
62Hxx	多元分析[参见60Exx]		Multivariate analysis [See also 60Exx]
62H05	特征和结构理论		Characterization and structure theory
62H10	统计分布		Distribution of statistics
62H11	方向数据; 空间统计学		Directional data; spatial statistics
62H12	估计		Estimation
62H15	假设检验		Hypothesis testing
62H17	列联表		Contingency tables
62H20	结合(相关、标准相关等)的测度		Measures of association (correlation, canonical correlation, etc.)
62H25	因子分析和主分量; 对应分析		Factor analysis and principal components; correspondence analysis
62H30	分类和判别; 聚类分析[参见68T10, 91C20]		Classification and discrimination; cluster analysis [See also 68T10, 91C20]
62H35	图像分析		Image analysis
62H86	多元分析和模糊性		Multivariate analysis and fuzziness
62H99	其它		None of the above, but in this section
62Jxx	线性推断, 回归		Linear inference, regression
62J02	一般非线性回归		General nonlinear regression
62J05	线性回归		Linear regression
62J07	岭回归; 收缩估计量		Ridge regression; shrinkage estimators
62J10	方差和协方差分析		Analysis of variance and covariance
62J12	广义线性模型		Generalized linear models
62J15	成对和多重比较		Paired and multiple comparisons
62J20	诊断学		Diagnostics
62J86	模糊性, 线性推断和回归		Fuzziness, and linear inference and regression
62J99	其它		None of the above, but in this section
62Kxx	实验设计[参见05Bxx]		Design of experiments [See also 05Bxx]
62K05	最优设计		Optimal designs
62K10	区组设计		Block designs
62K15	析因设计		Factorial designs
62K20	响应曲面设计		Response surface designs
62K25	稳健参数设计		Robust parameter designs
62K86	实验的模糊性和设计		Fuzziness and design of experiments
62K99	其它		None of the above, but in this section
62Lxx	序贯法		Sequential methods
62L05	序贯设计		Sequential design
62L10	序贯分析		Sequential analysis
62L12	序贯估计		Sequential estimation
62L15	最优停止[参见60G40, 91A60]		Optimal stopping [See also 60G40, 91A60]
62L20	随机逼近		Stochastic approximation
62L86	模糊性和序贯法		Fuzziness and sequential methods
62L99	其它		None of the above, but in this section
62Mxx	随机过程推断		Inference from stochastic processes
62M02	Markov过程: 假设检验		Markov processes: hypothesis testing
62M05	Markov过程: 估计		Markov processes: estimation
62M07	非Markov过程: 假设检验		Non-Markovian processes: hypothesis testing
62M09	非Markov过程: 估计		Non-Markovian processes: estimation
62M10	时间序列、自动相关、回归等[参见91B84]		Time series, auto-correlation, regression, etc. [See also 91B84]
62M15	谱分析		Spectral analysis
62M20	预报[参见60G25]; 滤波[参见60G35, 93E10, 93E11]		Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
62M30	空间过程		Spatial processes
62M40	随机场; 图象分析		Random fields; image analysis
62M45	神经网及相关方法		Neural nets and related approaches
62M86	来自随机过程和模糊性的推断		Inference from stochastic processes and fuzziness
62M99	其它		None of the above, but in this section
62Nxx	生存分析和截尾数据		Survival analysis and censored data
62N01	截尾数据模型		Censored data models
62N02	估计		Estimation
62N03	检验		Testing
62N05	可靠性和寿命试验[参见90B25]		Reliability and life testing [See also 90B25]
62N86	模糊性, 生存分析和截尾数据		Fuzziness, and survival analysis and censored data
62N99	其它		None of the above, but in this section
62Pxx	应用[参见90-XX, 91-XX, 92-XX]		Applications [See also 90-XX, 91-XX, 92-XX]
62P05	在精算学和金融数学的应用		Applications to actuarial sciences and financial mathematics
62P10	在生物学和医学科学的应用		Applications to biology and medical sciences
62P12	应用于环境及相关课题		Applications to environmental and related topics
62P15	在心理学方面的应用		Applications to psychology
62P20	在经济学方面的应用[参见91Bxx]		Applications to economics [See also 91Bxx]
62P25	在社会科学方面的应用		Applications to social sciences
62P30	应用于工程和工业		Applications in engineering and industry
62P35	应用于物理		Applications to physics
62P99	其它		None of the above, but in this section
62Qxx	统计表		Statistical tables
62Q05	统计表		Statistical tables
62Q99	其它		None of the above, but in this section
65-XX	数值分析		Numerical analysis
65-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
65-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
65-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
65-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
65-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
65-05	实验论文		Experimental papers
65-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
65Axx	表		Tables
65A05	表		Tables
65A99	其它		None of the above, but in this section
65Bxx	收敛性的加速		Acceleration of convergence
65B05	极限外推, 延迟校正		Extrapolation to the limit, deferred corrections
65B10	级数求和		Summation of series
65B15	Euler-Maclaurin公式		Euler-Maclaurin formula
65B99	其它		None of the above, but in this section
65Cxx	概率方法, 模拟和随机微分方程(理论方面, 见68U20和60H35)		Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35)
65C05	Monte Carlo方法		Monte Carlo methods
65C10	随机数生成		Random number generation
65C20	模型, 数值方法[参见68U20]		Models, numerical methods [See also 68U20]
65C30	随机微分和积分方程		Stochastic differential and integral equations
65C35	随机粒子法[参见82C80]		Stochastic particle methods [See also 82C80]
65C40	计算Markov链		Computational Markov chains
65C50	概率中的其它计算问题		Other computational problems in probability
65C60	统计学中的计算问题		Computational problems in statistics
65C99	其它		None of the above, but in this section
65Dxx	数值逼近和计算几何(基本算法)(理论, 见41-XX和68Uxx)		Numerical approximation and computational geometry (Primarily algorithms) (for theory, see 41-XX and 68Uxx)
65D05	插值		Interpolation
65D07	样条		Splines
65D10	光滑, 曲线拟合		Smoothing, curve fitting
65D15	函数逼近算法		Algorithms for functional approximation
65D17	计算机辅助设计(曲线和曲面的模型建立)[参见68U07]		Computer aided design (modeling of curves and surfaces) [See also 68U07]
65D18	计算机图形学, 图象分析和计算几何[参见51N05, 68U05]		Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05]
65D19	计算机中计算问题和机器人视觉		Computational issues in computer and robotic vision
65D20	特殊函数的计算, 表的构造[参见33F05]		Computation of special functions, construction of tables [See also 33F05]
65D25	数值微分法		Numerical differentiation
65D30	数值积分法		Numerical integration
65D32	求面积和体积公式		Quadrature and cubature formulas
65D99	其它		None of the above, but in this section
65Exx	复分析中的数值方法(位势论等)[共形映射的数值方法, 参见30C30]		Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30]
65E05	复分析中的数值方法(位势论等)[共形映射的数值方法, 参见30C30]		Numerical methods in complex analysis (potential theory, etc.) [For numerical methods in conformal mapping, see also 30C30]
65E99	其它		None of the above, but in this section
65Fxx	数值线性代数		Numerical linear algebra
65F05	线性系统和矩阵反演的直接法		Direct methods for linear systems and matrix inversion
65F08	迭代法的预条件子		Preconditioners for iterative methods
65F10	线性系统的迭代法[参见65N22]		Iterative methods for linear systems [See also 65N22]
65F15	特征值, 特征向量		Eigenvalues, eigenvectors
65F18	逆特征值问题		Inverse eigenvalue problems
65F20	超定组, 伪逆		Overdetermined systems, pseudoinverses
65F22	不适定性, 正则化		Ill-posedness, regularization
65F25	正交化		Orthogonalization
65F30	其它矩阵算法		Other matrix algorithms
65F35	矩阵范数, 条件作用, 比例[参见15A12, 15A60]		Matrix norms, conditioning, scaling [See also 15A12, 15A60]
65F40	行列式		Determinants
65F50	稀疏矩阵		Sparse matrices
65F60	矩阵指数和相似矩阵函数		Matrix exponential and similar matrix functions
65F99	其它		None of the above, but in this section
65Gxx	误差分析和区间分析		Error analysis and interval analysis
65G20	自动结果验证算法		Algorithms with automatic result verification
65G30	区间和有限算术		Interval and finite arithmetic
65G40	区间分析中的一般方法		General methods in interval analysis
65G50	舍入误差		Roundoff error
65G99	其它		None of the above, but in this section
65Hxx	非线性代数方程或超越方程		Nonlinear algebraic or transcendental equations
65H04	多项式方程的根		Roots of polynomial equations
65H05	单一方程		Single equations
65H10	方程组		Systems of equations
65H17	特征值, 特征向量[参见47Hxx, 47Jxx, 58C40, 58E07, 90C30]		Eigenvalues, eigenvectors [See also 47Hxx, 47Jxx, 58C40, 58E07, 90C30]
65H20	整体方法, 包括同伦法[参见58C30, 90C30]		Global methods, including homotopy approaches [See also 58C30, 90C30]
65H99	其它		None of the above, but in this section
65Jxx	抽象空间中的数值分析		Numerical analysis in abstract spaces
65J05	一般理论		General theory
65J08	抽象发展方程		Abstract evolution equations
65J10	线性算子方程(不用65Fxx)		Equations with linear operators (do not use 65Fxx)
65J15	非线性算子方程(不用65Hxx)		Equations with nonlinear operators (do not use 65Hxx)
65J20	不适定的问题; 正则化		Improperly posed problems; regularization
65J22	逆问题		Inverse problems
65J99	其它		None of the above, but in this section
65Kxx	数学规划, 最优化和变分法		Mathematical programming, optimization and variational techniques
65K05	数学规划法[参见90Cxx]		Mathematical programming methods [See also 90Cxx]
65K10	最优化和变分法[参见49Mxx, 93B40]		Optimization and variational techniques [See also 49Mxx, 93B40]
65K15	变分不等式及相关问题的数值方法		Numerical methods for variational inequalities and related problems
65K99	其它		None of the above, but in this section
65Lxx	常微分方程		Ordinary differential equations
65L03	泛函微分方程		Functional-differential equations
65L04	刚性方程		Stiff equations
65L05	初值问题		Initial value problems
65L06	多步法, Runge-Kutta法和外推法		Multistep, Runge-Kutta and extrapolation methods
65L07	解稳定性的数值研究		Numerical investigation of stability of solutions
65L08	不适定问题		Improperly posed problems
65L09	逆问题		Inverse problems
65L10	边值问题		Boundary value problems
65L11	奇异摄动问题		Singularly perturbed problems
65L12	有限差分法		Finite difference methods
65L15	特征值问题		Eigenvalue problems
65L20	数值方法的稳定性和收敛性		Stability and convergence of numerical methods
65L50	网格生成和加细		Mesh generation and refinement
65L60	有限元法, Rayleigh-Ritz法, Galerkin法和配置法		Finite elements, Rayleigh-Ritz, Galerkin and collocation methods
65L70	误差界		Error bounds
65L80	微分-代数方程的方法		Methods for differential-algebraic equations
65L99	其它		None of the above, but in this section
65Mxx	偏微分方程, 初值和不定常的初-边值问题		Partial differential equations, initial value and time-dependent initial-boundary value problems
65M06	有限差分法		Finite difference methods
65M08	有限体积法		Finite volume methods
65M12	数值方法的稳定性和收敛性		Stability and convergence of numerical methods
65M15	误差界		Error bounds
65M20	线方法		Method of lines
65M22	离散方程的解[参见65Fxx, 65Hxx]		Solution of discretized equations [See also 65Fxx, 65Hxx]
65M25	特征法		Method of characteristics
65M30	不适定问题		Improperly posed problems
65M32	逆问题		Inverse problems
65M38	边界元法		Boundary element methods
65M50	网格生成和加细		Mesh generation and refinement
65M55	多重网格法; 区域分解		Multigrid methods; domain decomposition
65M60	有限元法, Rayleigh-Ritz法和Galerkin法, 有限法		Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65M70	谱方法, 配置和相关方法		Spectral, collocation and related methods
65M75	概率方法、粒子法等		Probabilistic methods, particle methods, etc.
65M80	基本解、Green函数法等		Fundamental solutions, Green’s function methods, etc.
65M85	虚构区域法		Fictitious domain methods
65M99	其它		None of the above, but in this section
65Nxx	偏微分方程, 边值问题		Partial differential equations, boundary value problems
65N06	有限差分法		Finite difference methods
65N08	有限体积法		Finite volume methods
65N12	数值方法的稳定性和收敛性		Stability and convergence of numerical methods
65N15	误差界		Error bounds
65N20	不适定问题		Ill-posed problems
65N21	逆问题		Inverse problems
65N22	离散方程的解[参见65Fxx, 65Hxx]		Solution of discretized equations [See also 65Fxx, 65Hxx]
65N25	特征值问题		Eigenvalue problems
65N30	有限元法, Rayleigh-Ritz法和Galerkin法, 有限法		Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65N35	谱方法, 配置和相关方法		Spectral, collocation and related methods
65N38	边界元法		Boundary element methods
65N40	线方法		Method of lines
65N45	边界收缩法		Method of contraction of the boundary
65N50	网格生成和加细		Mesh generation and refinement
65N55	多重网格法; 区域分解		Multigrid methods; domain decomposition
65N75	概率方法、粒子法等		Probabilistic methods, particle methods, etc.
65N80	基本解、Green函数法等		Fundamental solutions, Green’s function methods, etc.
65N85	虚构区域法		Fictitious domain methods
65N99	其它		None of the above, but in this section
65Pxx	动力系统中的数值问题[参见37Mxx]		Numerical problems in dynamical systems [See also 37Mxx]
65P10	包括辛积分器的Hamilton系统		Hamiltonian systems including symplectic integrators
65P20	数值混沌		Numerical chaos
65P30	分歧问题		Bifurcation problems
65P40	非线性稳定性		Nonlinear stabilities
65P99	其它		None of the above, but in this section
65Qxx	差分和泛函方程, 递推关系		Difference and functional equations, recurrence relations
65Q10	差分方程		Difference equations
65Q20	泛函方程		Functional equations
65Q30	递推关系		Recurrence relations
65Q99	其它		None of the above, but in this section
65Rxx	积分方程, 积分变换		Integral equations, integral transforms
65R10	积分变换		Integral transforms
65R20	积分方程		Integral equations
65R30	不适定问题		Improperly posed problems
65R32	逆问题		Inverse problems
65R99	其它		None of the above, but in this section
65Sxx	图解法		Graphical methods
65S05	图解法		Graphical methods
65S99	其它		None of the above, but in this section
65Txx	Fourier分析中的数值方法		Numerical methods in Fourier analysis
65T40	三角逼近和插值		Trigonometric approximation and interpolation
65T50	离散和快速Fourier变换		Discrete and fast Fourier transforms
65T60	小波		Wavelets
65T99	其它		None of the above, but in this section
65Yxx	数值算法的计算机方面		Computer aspects of numerical algorithms
65Y04	计算机运算的算法等[参见68M07]		Algorithms for computer arithmetic, etc. [See also 68M07]
65Y05	并行计算		Parallel computation
65Y10	具体结构类算法		Algorithms for specific classes of architectures
65Y15	软件包方法		Packaged methods
65Y20	数值算法的复杂性和性能[参见68Q25]		Complexity and performance of numerical algorithms [See also 68Q25]
65Y99	其它		None of the above, but in this section
65Zxx	应用于物理		Applications to physics
65Z05	应用于物理		Applications to physics
65Z99	其它		None of the above, but in this section
68-XX	计算机科学(特殊数学领域中涉及机器计算和程序的论文, 见有关领域-04部分)		Computer science (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
68-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
68-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
68-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
68-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
68-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
68-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
68Mxx	计算机系统结构		Computer system organization
68M01	一般理论		General
68M07	计算机体系结构的数学问题		Mathematical problems of computer architecture
68M10	网络设计和通信[参见68R10, 90B18]		Network design and communication [See also 68R10, 90B18]
68M11	与互联网相关的议题[参见68U35]		Internet topics [See also 68U35]
68M12	网络协议		Network protocols
68M14	分布系统		Distributed systems
68M15	可靠性, 检测和容错[参见94C12]		Reliability, testing and fault tolerance [See also 94C12]
68M20	性能评估; 排队; 调度[参见60K25, 90Bxx]		Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]
68M99	其它		None of the above, but in this section
68Nxx	软件		Software
68N01	一般理论		General
68N15	程序设计语言		Programming languages
68N17	逻辑程序设计		Logic programming
68N18	功能程序设计和λ演算[参见03B40]		Functional programming and lambda calculus [See also 03B40]
68N19	其它程序设计技术(面向对象、顺序的、并行的、自动的等)		Other programming techniques (object-oriented, sequential, concurrent, automatic, etc.)
68N20	编译程序和解释程序		Compilers and interpreters
68N25	操作系统		Operating systems
68N30	软件工程的数学方面(规格、检验、度量、需求等)		Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
68N99	其它		None of the above, but in this section
68Pxx	数据理论		Theory of data
68P01	一般理论		General
68P05	数据结构		Data structures
68P10	搜索和分类		Searching and sorting
68P15	数据库理论		Database theory
68P20	信息存储和检索		Information storage and retrieval
68P25	数据加密[参见94A60, 81P94]		Data encryption [See also 94A60, 81P94]
68P30	编码和信息理论(通信压缩、通信紧致、通信模型、编码方案等)[参见94Axx]		Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) [See also 94Axx]
68P99	其它		None of the above, but in this section
68Qxx	计算理论		Theory of computing
68Q01	一般理论		General
68Q05	计算模型(Turing机等)[参见03D10, 68Q12, 81P68]		Models of computation (Turing machines, etc.) [See also 03D10, 68Q12, 81P68]
68Q10	计算模式(非确定性、并行的、交互的、概率的等)[参见68Q85]		Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) [See also 68Q85]
68Q12	量子算法与复杂性[参见68Q05, 81P68]		Quantum algorithms and complexity [See also 68Q05, 81P68]
68Q15	复杂性类别(分层、复杂性类别中的关系等)[参见03D15, 68Q17, 68Q19]		Complexity classes (hierarchies, relations among complexity classes, etc.) [See also 03D15, 68Q17, 68Q19]
68Q17	计算问题的难度(下界、完全性、逼近的难度等)[参见68Q15]		Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) [See also 68Q15]
68Q19	描述复杂性和有限模型[参见03C13]		Descriptive complexity and finite models [See also 03C13]
68Q25	算法分析和问题复杂性[参见68W40]		Analysis of algorithms and problem complexity [See also 68W40]
68Q30	算法信息理论(Kolmogorov复杂性等)[参见03D32]		Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32]
68Q32	计算学习理论[参见68T05]		Computational learning theory [See also 68T05]
68Q42	文法和重写系统		Grammars and rewriting systems
68Q45	形式语言和自动机[参见03D05, 68Q70, 94A45]		Formal languages and automata [See also 03D05, 68Q70, 94A45]
68Q55	语义学[参见03B70, 06B35, 18C50]		Semantics [See also 03B70, 06B35, 18C50]
68Q60	说明和检验(程序逻辑、模型校验等)[参见03B70]		Specification and verification (program logics, model checking, etc.) [See also 03B70]
68Q65	抽象数据类型; 代数说明[参见18C50]		Abstract data types; algebraic specification [See also 18C50]
68Q70	语言和自动机的代数理论[参见18B20, 20M35]		Algebraic theory of languages and automata [See also 18B20, 20M35]
68Q80	细胞自动机[参见37B15]		Cellular automata [See also 37B15]
68Q85	并行和分布计算的模型和方法(进程代数、双模拟、转移网等)		Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
68Q87	计算机科学中的概率(算法分析、随机结构、相变等)[参见68W20, 68W40]		Probability in computer science (algorithm analysis, random structures, phase transitions, etc.) [See also 68W20, 68W40]
68Q99	其它		None of the above, but in this section
68Rxx	同计算机科学有关的离散数学		Discrete mathematics in relation to computer science
68R01	一般理论		General
68R05	组合学		Combinatorics
68R10	图论(包括制图)[参见05Cxx, 90B10, 90B35, 90C35]		Graph theory (including graph drawing) [See also 05Cxx, 90B10, 90B35, 90C35]
68R15	字的组合学		Combinatorics on words
68R99	其它		None of the above, but in this section
68Txx	人工智能		Artificial intelligence
68T01	一般理论		General
68T05	学习和自适应系统[参见68Q32, 91E40]		Learning and adaptive systems [See also 68Q32, 91E40]
68T10	模式识别, 语音识别(聚类分析, 见62H30)		Pattern recognition, speech recognition (For cluster analysis, see 62H30)
68T15	定理证明(推论、归结等)[参见03B35]		Theorem proving (deduction, resolution, etc.) [See also 03B35]
68T20	问题求解(启发式的、搜索策略等)		Problem solving (heuristics, search strategies, etc.)
68T27	人工智能中的逻辑		Logic in artificial intelligence
68T30	知识表示		Knowledge representation
68T35	语言和软件系统(基于知识系统、专家系统等)		Languages and software systems (knowledge-based systems, expert systems, etc.)
68T37	不确定性推理		Reasoning under uncertainty
68T40	机器人[参见93C85]		Robotics [See also 93C85]
68T42	代理技术		Agent technology
68T45	机器视觉和图像理解		Machine vision and scene understanding
68T50	自然语言处理[参见03B65]		Natural language processing [See also 03B65]
68T99	其它		None of the above, but in this section
68Uxx	计算方法论和应用		Computing methodologies and applications
68U01	一般理论		General
68U05	计算机制图; 计算几何[参见65D18]		Computer graphics; computational geometry [See also 65D18]
68U07	计算机辅助设计[参见65D17]		Computer-aided design [See also 65D17]
68U10	图象处理		Image processing
68U15	文本处理; 数学排印		Text processing; mathematical typography
68U20	模拟[参见65Cxx]		Simulation [See also 65Cxx]
68U35	信息系统(超文本导航、接口、决策支持等)[参见68M11]		Information systems (hypertext navigation, interfaces, decision support, etc.) [See also 68M11]
68U99	其它		None of the above, but in this section
68Wxx	算法(数值算法, 见65-XX; 组合论和图论, 见05C85, 68Rxx)		Algorithms (For numerical algorithms, see 65-XX; for combinatorics and graph theory, see 05C85, 68Rxx)
68W01	一般理论		General
68W05	非数值算法		Nonnumerical algorithms
68W10	并行算法		Parallel algorithms
68W15	分布算法		Distributed algorithms
68W20	随机化算法		Randomized algorithms
68W25	近似算法		Approximation algorithms
68W27	在线算法		Online algorithms
68W30	符号计算和代数计算[参见11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]		Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10]
68W32	串算法		Algorithms on strings
68W35	超大规模集成电路算法		VLSI algorithms
68W40	算法分析[参见68Q25]		Analysis of algorithms [See also 68Q25]
68W99	其它		None of the above, but in this section
70-XX	质点和系统力学(相对论力学, 见83A05, 83C10; 统计力学, 见82-XX)		Mechanics of particles and systems (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX)
70-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
70-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
70-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
70-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
70-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
70-05	实验工作		Experimental work
70-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
70-08	计算方法		Computational methods
70Axx	公理系统, 基础		Axiomatics, foundations
70A05	公理系统, 基础		Axiomatics, foundations
70A99	其它		None of the above, but in this section
70Bxx	运动学[参见53A17]		Kinematics [See also 53A17]
70B05	质点运动学		Kinematics of a particle
70B10	刚体运动学		Kinematics of a rigid body
70B15	力学, 机器人[参见68T40, 70Q05, 93C85]		Mechanisms, robots [See also 68T40, 70Q05, 93C85]
70B99	其它		None of the above, but in this section
70Cxx	静力学		Statics
70C20	静力学		Statics
70C99	其它		None of the above, but in this section
70Exx	刚体动力学和多体系统动力学		Dynamics of a rigid body and of multibody systems
70E05	陀螺仪的运动		Motion of the gyroscope
70E15	刚体自由运动[参见70M20]		Free motion of a rigid body [See also 70M20]
70E17	具有定点的刚体运动		Motion of a rigid body with a fixed point
70E18	同固体界面接触的刚体运动[参见70F25]		Motion of a rigid body in contact with a solid surface [See also 70F25]
70E20	刚体动力学的摄动方法		Perturbation methods for rigid body dynamics
70E40	运动的可积情形		Integrable cases of motion
70E45	较高维上推广		Higher-dimensional generalizations
70E50	稳定性问题		Stability problems
70E55	多体系统动力学		Dynamics of multibody systems
70E60	机器人动力学和控制[参见68T40, 70Q05, 93C85]		Robot dynamics and control [See also 68T40, 70Q05, 93C85]
70E99	其它		None of the above, but in this section
70Fxx	质点系统动力学, 包括天体力学		Dynamics of a system of particles, including celestial mechanics
70F05	二体问题		Two-body problems
70F07	三体问题		Three-body problems
70F10	n-体问题		n-body problems
70F15	天体力学		Celestial mechanics
70F16	天体力学中的碰撞, 正则化		Collisions in celestial mechanics, regularization
70F17	逆问题		Inverse problems
70F20	完整系统		Holonomic systems
70F25	非完整系统		Nonholonomic systems
70F35	刚体或伪刚体的碰撞		Collision of rigid or pseudo-rigid bodies
70F40	摩擦问题		Problems with friction
70F45	无限质点系统		Infinite particle systems
70F99	其它		None of the above, but in this section
70Gxx	一般模型、途径和方法[参见37-XX]		General models, approaches, and methods [See also 37-XX]
70G10	广义坐标; 事件空间, 冲击能空间, 构形空间, 状态空间或相空间		Generalized coordinates; event, impulse-energy, configuration, state, or phase space
70G40	拓扑方法和微分拓扑方法		Topological and differential-topological methods
70G45	微分几何方法(张量、联络、辛的、Poisson、接触、Riemann、非完整等)[参见53Cxx, 53Dxx, 58Axx]		Differential-geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) [See also 53Cxx, 53Dxx, 58Axx]
70G55	代数几何方法		Algebraic geometry methods
70G60	动力系统方法		Dynamical systems methods
70G65	对称, Lie群和Lie代数方法		Symmetries, Lie-group and Lie-algebra methods
70G70	泛函分析方法		Functional-analytic methods
70G75	变分法		Variational methods
70G99	其它		None of the above, but in this section
70Hxx	Hamilton和Lagrange力学[参见37Jxx]		Hamiltonian and Lagrangian mechanics [See also 37Jxx]
70H03	Lagrange方程		Lagrange’s equations
70H05	Hamilton方程		Hamilton’s equations
70H06	完全可积系统和积分方法		Completely integrable systems and methods of integration
70H07	不可积系统		Nonintegrable systems
70H08	近可积Hamilton系统, KAM理论		Nearly integrable Hamiltonian systems, KAM theory
70H09	扰动理论		Perturbation theories
70H11	绝热不变量		Adiabatic invariants
70H12	周期解和概周期解		Periodic and almost periodic solutions
70H14	稳定性问题		Stability problems
70H15	标准变换和辛变换		Canonical and symplectic transformations
70H20	Hamilton-Jacobi方程		Hamilton-Jacobi equations
70H25	Hamilton原理		Hamilton’s principle
70H30	其它变分原理		Other variational principles
70H33	对称律, 守恒律, 逆对称, 不变流形及其分歧, 约化		Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction
70H40	相对论动力学		Relativistic dynamics
70H45	约束动力学, Dirac约束理论[参见70F20, 70F25, 70Gxx]		Constrained dynamics, Dirac’s theory of constraints [See also 70F20, 70F25, 70Gxx]
70H50	更高阶理论		Higher-order theories
70H99	其它		None of the above, but in this section
70Jxx	线性振动理论		Linear vibration theory
70J10	模态分析		Modal analysis
70J25	稳定性		Stability
70J30	自由运动		Free motions
70J35	受迫运动		Forced motions
70J40	参量共振		Parametric resonances
70J50	结构振动问题的离散化系统		Systems arising from the discretization of structural vibration problems
70J99	其它		None of the above, but in this section
70Kxx	非线性动力学[参见34Cxx, 37-XX]		Nonlinear dynamics [See also 34Cxx, 37-XX]
70K05	相位平面分析, 极限环		Phase plane analysis, limit cycles
70K20	稳定性		Stability
70K25	自由运动		Free motions
70K28	参量共振		Parametric resonances
70K30	非线性共振		Nonlinear resonances
70K40	受迫运动		Forced motions
70K42	平衡轨道和周期轨道		Equilibria and periodic trajectories
70K43	拟周期运动和不变环面		Quasi-periodic motions and invariant tori
70K44	同宿轨道和异宿轨道		Homoclinic and heteroclinic trajectories
70K45	标准型		Normal forms
70K50	分叉和不稳定性		Bifurcations and instability
70K55	随机性转移(混沌性态)[参见37D45]		Transition to stochasticity (chaotic behavior) [See also 37D45]
70K60	一般扰动格式		General perturbation schemes
70K65	扰动平均		Averaging of perturbations
70K70	慢速和快速运动系统		Systems with slow and fast motions
70K75	非线性模式		Nonlinear modes
70K99	其它		None of the above, but in this section
70Lxx	随机振动[参见74H50]		Random vibrations [See also 74H50]
70L05	随机振动[参见74H50]		Random vibrations [See also 74H50]
70L99	其它		None of the above, but in this section
70Mxx	轨道力学		Orbital mechanics
70M20	轨道力学		Orbital mechanics
70M99	其它		None of the above, but in this section
70Pxx	可变质量, 火箭		Variable mass, rockets
70P05	可变质量, 火箭		Variable mass, rockets
70P99	其它		None of the above, but in this section
70Qxx	力学系统的控制[参见60Gxx, 60Jxx]		Control of mechanical systems [See also 60Gxx, 60Jxx]
70Q05	力学系统的控制[参见60Gxx, 60Jxx]		Control of mechanical systems [See also 60Gxx, 60Jxx]
70Q99	其它		None of the above, but in this section
70Sxx	经典场论[参见37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]		Classical field theories [See also 37Kxx, 37Lxx, 78-XX, 81Txx, 83-XX]
70S05	Lagrange形式体系, Hamilton形式体系		Lagrangian formalism and Hamiltonian formalism
70S10	对称律和守恒律		Symmetries and conservation laws
70S15	Yang-Mills和其它规范理论		Yang-Mills and other gauge theories
70S20	更一般非量子场论		More general nonquantum field theories
70S99	其它		None of the above, but in this section
74-XX	变形固体力学		Mechanics of deformable solids
74-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
74-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
74-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
74-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
74-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
74-05	实验工作		Experimental work
74-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
74Axx	连续固体力学的概论, 公理系统, 基础		Generalities, axiomatics, foundations of continuum mechanics of solids
74A05	变形运动学		Kinematics of deformation
74A10	应力		Stress
74A15	热力学		Thermodynamics
74A20	本构函数理论		Theory of constitutive functions
74A25	分子理论, 统计理论和动力学理论		Molecular, statistical, and kinetic theories
74A30	非单纯材料		Nonsimple materials
74A35	极性材料		Polar materials
74A40	随机材料和合成材料		Random materials and composite materials
74A45	破裂和破坏理论		Theories of fracture and damage
74A50	结构表面, 结构界面, 共存相		Structured surfaces and interfaces, coexistent phases
74A55	摩擦理论		Theories of friction (tribology)
74A60	微观力学理论		Micromechanical theories
74A65	反应材料		Reactive materials
74A99	其它		None of the above, but in this section
74Bxx	弹性材料		Elastic materials
74B05	经典线性弹性学		Classical linear elasticity
74B10	有初始应力的线性弹性学		Linear elasticity with initial stresses
74B15	形变状态(小形变迭加在大形变上)线性化方程		Equations linearized about a deformed state (small deformations superposed on large)
74B20	非线性弹性学		Nonlinear elasticity
74B99	其它		None of the above, but in this section
74Cxx	可塑性材料, 应力速率和内部可变型材料		Plastic materials, materials of stress-rate and internal-variable type
74C05	小应变, 速率无关理论(包括刚塑性和弹塑性材料)		Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74C10	小应变, 速率相关理论(包括粘塑性理论)		Small-strain, rate-dependent theories (including theories of viscoplasticity)
74C15	大应变, 速率无关理论(包括非线性塑性力学)		Large-strain, rate-independent theories (including nonlinear plasticity)
74C20	大应变, 速率相关理论		Large-strain, rate-dependent theories
74C99	其它		None of the above, but in this section
74Dxx	应变速率型材料和历史型材料, 其它具有记忆的材料(包括粘性阻尼弹性材料, 各种粘弹性材料)		Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
74D05	线性本构方程		Linear constitutive equations
74D10	非线性本构方程		Nonlinear constitutive equations
74D99	其它		None of the above, but in this section
74Exx	特殊处理的材料性质		Material properties given special treatment
74E05	非均匀材料		Inhomogeneity
74E10	各向异性		Anisotropy
74E15	晶状结构		Crystalline structure
74E20	粒度		Granularity
74E25	织构		Texture
74E30	合成和混合性质		Composite and mixture properties
74E35	随机结构		Random structure
74E40	化学结构		Chemical structure
74E99	其它		None of the above, but in this section
74Fxx	固体力学与其它效应的耦合		Coupling of solid mechanics with other effects
74F05	热效应		Thermal effects
74F10	流体-固体相互作用(包括气动力弹性和流体弹性、多孔性等)		Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74F15	电磁效应		Electromagnetic effects
74F20	混合效应		Mixture effects
74F25	化学和活性效应		Chemical and reactive effects
74F99	其它		None of the above, but in this section
74Gxx	平衡(稳态)问题		Equilibrium (steady-state) problems
74G05	显式解		Explicit solutions
74G10	解的解析逼近(摄动法、渐近线法、级数等)		Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
74G15	解的数值逼近		Numerical approximation of solutions
74G20	解的局部存在性(接近一给定解)		Local existence of solutions (near a given solution)
74G25	解的整体存在性		Global existence of solutions
74G30	解的唯一性		Uniqueness of solutions
74G35	解的重数		Multiplicity of solutions
74G40	解的正则性		Regularity of solutions
74G45	解的界		Bounds for solutions
74G50	Saint-Venant原理		Saint-Venant’s principle
74G55	解的定性性态		Qualitative behavior of solutions
74G60	分叉和屈曲		Bifurcation and buckling
74G65	能量极小化		Energy minimization
74G70	应力集中, 奇异性		Stress concentrations, singularities
74G75	逆问题		Inverse problems
74G99	其它		None of the above, but in this section
74Hxx	动力学问题		Dynamical problems
74H05	显式解		Explicit solutions
74H10	解的解析逼近(扰动法、渐近线法、级数等)		Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.)
74H15	解的数值逼近		Numerical approximation of solutions
74H20	解的存在性		Existence of solutions
74H25	解的唯一性		Uniqueness of solutions
74H30	解的正则性		Regularity of solutions
74H35	奇异性, 爆破, 应力集中		Singularities, blowup, stress concentrations
74H40	解的长时间性态		Long-time behavior of solutions
74H45	振荡		Vibrations
74H50	随机振荡		Random vibrations
74H55	稳定性		Stability
74H60	动力学分歧		Dynamical bifurcation
74H65	混沌性态		Chaotic behavior
74H99	其它		None of the above, but in this section
74Jxx	波		Waves
74J05	线性波		Linear waves
74J10	体波		Bulk waves
74J15	表面波		Surface waves
74J20	波散射		Wave scattering
74J25	逆问题		Inverse problems
74J30	非线性波		Nonlinear waves
74J35	孤波		Solitary waves
74J40	激波和相关不连续性		Shocks and related discontinuities
74J99	其它		None of the above, but in this section
74Kxx	薄体, 结构		Thin bodies, structures
74K05	弦		Strings
74K10	连杆(梁、柱、轴、拱、环等)		Rods (beams, columns, shafts, arches, rings, etc.)
74K15	薄膜		Membranes
74K20	板		Plates
74K25	壳体		Shells
74K30	接合		Junctions
74K35	薄膜		Thin films
74K99	其它		None of the above, but in this section
74Lxx	固体力学的特殊子域		Special subfields of solid mechanics
74L05	地球物理固体力学[参见86-XX]		Geophysical solid mechanics [See also 86-XX]
74L10	土力学和岩石力学		Soil and rock mechanics
74L15	生物固体力学[参见92C10]		Biomechanical solid mechanics [See also 92C10]
74L99	其它		None of the above, but in this section
74Mxx	问题的特殊类型		Special kinds of problems
74M05	控制, 开关和设备(“智能材料”)[参见93Cxx]		Control, switches and devices (“smart materials”) [See also 93Cxx]
74M10	摩擦		Friction
74M15	接触		Contact
74M20	冲击		Impact
74M25	微观力学		Micromechanics
74M99	其它		None of the above, but in this section
74Nxx	固体中的相变[参见74A50, 80Axx, 82B26, 82C26]		Phase transformations in solids [See also 74A50, 80Axx, 82B26, 82C26]
74N05	晶体		Crystals
74N10	位移变换		Displacive transformations
74N15	微观结构分析		Analysis of microstructure
74N20	相边界动力学		Dynamics of phase boundaries
74N25	扩散的变换		Transformations involving diffusion
74N30	滞后的问题		Problems involving hysteresis
74N99	其它		None of the above, but in this section
74Pxx	最优化[参见49Qxx]		Optimization [See also 49Qxx]
74P05	一致或权最优化		Compliance or weight optimization
74P10	其它性质的最优化		Optimization of other properties
74P15	拓扑方法		Topological methods
74P20	几何方法		Geometrical methods
74P99	其它		None of the above, but in this section
74Qxx	均匀化, 有效特征的测定		Homogenization, determination of effective properties
74Q05	平衡(衡态)问题的均匀化		Homogenization in equilibrium problems
74Q10	动力学问题的均匀性和振动		Homogenization and oscillations in dynamical problems
74Q15	有效本构方程		Effective constitutive equations
74Q20	有效特征界		Bounds on effective properties
74Q99	其它		None of the above, but in this section
74Rxx	裂纹和损伤		Fracture and damage
74R05	脆性损伤		Brittle damage
74R10	脆性裂纹		Brittle fracture
74R15	高速裂纹		High-velocity fracture
74R20	内摩擦裂纹和损伤		Anelastic fracture and damage
74R99	其它		None of the above, but in this section
74Sxx	数值方法[参见65-XX, 74G15, 74H15]		Numerical methods [See also 65-XX, 74G15, 74H15]
74S05	有限元(方)法		Finite element methods
74S10	有限体积(方)法		Finite volume methods
74S15	边界元(方)法		Boundary element methods
74S20	有限差分(方)法		Finite difference methods
74S25	谱(方)法和相关方法		Spectral and related methods
74S30	其它数值(方)法		Other numerical methods
74S60	随机方法		Stochastic methods
74S70	复变量(方)法		Complex variable methods
74S99	其它		None of the above, but in this section
76-XX	流体力学(一般连续力学, 见74Axx或74-XX其它部分)		Fluid mechanics (For general continuum mechanics, see 74Axx, or other parts of 74-XX)
76-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
76-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
76-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
76-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
76-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
76-05	实验工作		Experimental work
76-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
76Axx	基础, 结构方程, 流变学		Foundations, constitutive equations, rheology
76A02	流体力学基础		Foundations of fluid mechanics
76A05	非Newton流体		Non-Newtonian fluids
76A10	粘弹性流体		Viscoelastic fluids
76A15	液晶[参见82D30]		Liquid crystals [See also 82D30]
76A20	流体薄膜		Thin fluid films
76A25	超流体(经典方面)		Superfluids (classical aspects)
76A99	其它		None of the above, but in this section
76Bxx	不可压缩非粘滞性流体		Incompressible inviscid fluids
76B03	存在性, 唯一性和正则性理论[参见35Q35]		Existence, uniqueness, and regularity theory [See also 35Q35]
76B07	自由界面位势流		Free-surface potential flows
76B10	射流和空腔, 空化, 自由流线理论, 水-入口问题, 机翼和水翼理论, 冲激		Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76B15	水波, 重力波; 弥散和散射, 非线性相互作用[参见35Q30]		Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30]
76B20	船波		Ship waves
76B25	孤波[参见35C11]		Solitary waves [See also 35C11]
76B45	毛细现象(表面张力)[参见76D45]		Capillarity (surface tension) [See also 76D45]
76B47	涡流		Vortex flows
76B55	内部波		Internal waves
76B60	大气波[参见86A10]		Atmospheric waves [See also 86A10]
76B65	Rossby波[参见86A05, 86A10]		Rossby waves [See also 86A05, 86A10]
76B70	非粘滞性流体中的层次效应		Stratification effects in inviscid fluids
76B75	流量控制和最优化[参见49Q10, 93C20, 93C95]		Flow control and optimization [See also 49Q10, 93C20, 93C95]
76B99	其它		None of the above, but in this section
76Dxx	不可压缩粘滞流体		Incompressible viscous fluids
76D03	存在性, 唯一性和正则性理论[参见35Q30]		Existence, uniqueness, and regularity theory [See also 35Q30]
76D05	Navier-Stokes方程		Navier-Stokes equations [See also 35Q30]
76D06	Navier-Stokes和相关方程的统计解[参见60H30, 76M35]		Statistical solutions of Navier-Stokes and related equations [See also 60H30, 76M35]
76D07	Stokes流和相关(Oseen等)流		Stokes and related (Oseen, etc.) flows
76D08	润滑理论		Lubrication theory
76D09	粘(滞)性-非粘(滞)性相互作用		Viscous-inviscid interaction
76D10	边界层理论, 分离和再附着, 高阶效应		Boundary-layer theory, separation and reattachment, higher-order effects
76D17	粘(滞)性涡流		Viscous vortex flows
76D25	尾流和射流		Wakes and jets
76D27	其它自由-边界流; Hele-Shaw流		Other free-boundary flows; Hele-Shaw flows
76D33	波		Waves
76D45	毛细现象(表面张力)[参见76B45]		Capillarity (surface tension) [See also 76B45]
76D50	粘(滞)性流中的层次效应		Stratification effects in viscous fluids
76D55	流量控制和最优化[参见49Q10, 93C20, 93C95]		Flow control and optimization [See also 49Q10, 93C20, 93C95]
76D99	其它		None of the above, but in this section
76Exx	流体动力学的稳定性		Hydrodynamic stability
76E05	平行剪切流		Parallel shear flows
76E06	对流		Convection
76E07	旋转		Rotation
76E09	不平行流的稳定性和不稳定性		Stability and instability of nonparallel flows
76E15	绝对和对流的不稳定性和稳定性		Absolute and convective instability and stability
76E17	界面稳定性和不稳定性		Interfacial stability and instability
76E19	(可)压缩性效应		Compressibility effects
76E20	地球物理学和天体物理学流的稳定性和不稳定性		Stability and instability of geophysical and astrophysical flows
76E25	磁流体动力和电流体动力流的稳定性的不稳定性		Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E30	非线性效应		Nonlinear effects
76E99	其它		None of the above, but in this section
76Fxx	湍流[参见37-XX, 60Gxx, 60Jxx]		Turbulence [See also 37-XX, 60Gxx, 60Jxx]
76F02	基础		Fundamentals
76F05	各向同性湍流; 齐次湍流		Isotropic turbulence; homogeneous turbulence
76F06	向湍流的转换		Transition to turbulence
76F10	剪切流		Shear flows
76F20	湍流的动力学系统方法[参见37-XX]		Dynamical systems approach to turbulence [See also 37-XX]
76F25	湍流输运, 混合		Turbulent transport, mixing
76F30	重正规化和其它场论方法[参见81T99]		Renormalization and other field-theoretical methods [See also 81T99]
76F35	对流湍流[参见76E15, 76Rxx]		Convective turbulence [See also 76E15, 76Rxx]
76F40	湍流边界层		Turbulent boundary layers
76F45	层次效应		Stratification effects
76F50	(可)压缩性效应		Compressibility effects
76F55	统计湍流建模 [参见76M35]		Statistical turbulence modeling [See also 76M35]
76F60	k-ε建模		k-ε modeling
76F65	湍流直接数值模拟和大涡流模拟		Direct numerical and large eddy simulation of turbulence
76F70	湍流控制		Control of turbulent flows
76F99	其它		None of the above, but in this section
76Gxx	一般空气动力学和亚音速流		General aerodynamics and subsonic flows
76G25	一般空气动力学和亚音速流		General aerodynamics and subsonic flows
76G99	其它		None of the above, but in this section
76Hxx	跨音速流		Transonic flows
76H05	跨音速流		Transonic flows
76H99	其它		None of the above, but in this section
76Jxx	超音速流		Supersonic flows
76J20	超音速流		Supersonic flows
76J99	其它		None of the above, but in this section
76Kxx	高超音速流		Hypersonic flows
76K05	高超音速流		Hypersonic flows
76K99	其它		None of the above, but in this section
76Lxx	激波和爆炸波[参见35L67]		Shock waves and blast waves [See also 35L67]
76L05	激波和爆炸波[参见35L67]		Shock waves and blast waves [See also 35L67]
76L99	其它		None of the above, but in this section
76Mxx	流体力学的基本方法[参见65-XX]		Basic methods in fluid mechanics [See also 65-XX]
76M10	有限元法		Finite element methods
76M12	有限体积法		Finite volume methods
76M15	边界元法		Boundary element methods
76M20	有限差分法		Finite difference methods
76M22	谱方法		Spectral methods
76M23	涡流方法		Vortex methods
76M25	其它数值方法		Other numerical methods
76M27	目测算法		Visualization algorithms
76M28	粒子方法和晶格-气体法		Particle methods and lattice-gas methods
76M30	变分法		Variational methods
76M35	随机分析		Stochastic analysis
76M40	复变量法		Complex-variables methods
76M45	渐近方法, 奇摄动		Asymptotic methods, singular perturbations
76M50	均匀性		Homogenization
76M55	维数分析和相似性		Dimensional analysis and similarity
76M60	对称分析, Lie群和代数法		Symmetry analysis, Lie group and algebra methods
76M99	其它		None of the above, but in this section
76Nxx	可压缩流体和气体动力学, 一般问题		Compressible fluids and gas dynamics, general
76N10	存在性, 唯一性和正则性理论[参见35L60, 35L65, 35Q30]		Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]
76N15	气体动力学, 一般问题		Gas dynamics, general
76N17	粘(滞)性-非粘(滞)性相互作用		Viscous-inviscid interaction
76N20	边界层理论		Boundary-layer theory
76N25	流(量)控制和最优化		Flow control and optimization
76N99	其它		None of the above, but in this section
76Pxx	稀薄气流, Boltzmann方程[参见82B40, 82C40, 82D05]		Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
76P05	稀薄气流, Boltzmann方程[参见82B40, 82C40, 82D05]		Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
76P99	其它		None of the above, but in this section
76Qxx	水声学和大气声学		Hydro- and aero-acoustics
76Q05	水声学和大气声学		Hydro- and aero-acoustics
76Q99	其它		None of the above, but in this section
76Rxx	扩散和对流		Diffusion and convection
76R05	受迫对流		Forced convection
76R10	自由对流		Free convection
76R50	扩散[参见60J60]		Diffusion [See also 60J60]
76R99	其它		None of the above, but in this section
76Sxx	多孔介质中的流; 滤波; 渗流		Flows in porous media; filtration; seepage
76S05	多孔介质中的流; 滤波; 渗流		Flows in porous media; filtration; seepage
76S99	其它		None of the above, but in this section
76Txx	两相流和多相流		Two-phase and multiphase flows
76T10	液-气两相流, 起泡流		Liquid-gas two-phase flows, bubbly flows
76T15	粉尘-气体两相流		Dusty-gas two-phase flows
76T20	悬浮物		Suspensions
76T25	粒状流[参见74C99, 74E20]		Granular flows [See also 74C99, 74E20]
76T30	三相或多相流		Three or more component flows
76T99	其它		None of the above, but in this section
76Uxx	旋转流体		Rotating fluids
76U05	旋转流体		Rotating fluids
76U99	其它		None of the above, but in this section
76Vxx	流中的反应效应[参见80A32]		Reaction effects in flows [See also 80A32]
76V05	流中的反应效应[参见80A32]		Reaction effects in flows [See also 80A32]
76V99	其它		None of the above, but in this section
76Wxx	磁流体动力学和电流体动力学		Magnetohydrodynamics and electrohydrodynamics
76W05	磁流体动力学和电流体动力学		Magnetohydrodynamics and electrohydrodynamics
76W99	其它		None of the above, but in this section
76Xxx	电磁场中的电离气流; 等离子流[参见82D10]		Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]
76X05	电磁场中的电离气流; 等离子流[参见82D10]		Ionized gas flow in electromagnetic fields; plasmic flow [See also 82D10]
76X99	其它		None of the above, but in this section
76Yxx	量子流体动力学和相对论流体动力学[参见82D50, 83C55, 85A30]		Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]
76Y05	量子流体动力学和相对论流体动力学[参见82D50, 83C55, 85A30]		Quantum hydrodynamics and relativistic hydrodynamics [See also 82D50, 83C55, 85A30]
76Y99	其它		None of the above, but in this section
76Zxx	生物流体力学[参见74F10, 74L15, 92Cxx]		Biological fluid mechanics [See also 74F10, 74L15, 92Cxx]
76Z05	生理学流[参见92C35]		Physiological flows [See also 92C35]
76Z10	水和空气中的生物推力		Biopropulsion in water and in air
76Z99	其它		None of the above, but in this section
78-XX	光学, 电磁理论(量子光学, 见81V80)		Optics, electromagnetic theory (For quantum optics, see 81V80)
78-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
78-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
78-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
78-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
78-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
78-05	实验工作		Experimental work
78-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
78Axx	一般理论		General
78A02	基础		Foundations
78A05	几何光学		Geometric optics
78A10	物理光学		Physical optics
78A15	电子光学		Electron optics
78A20	空间电波		Space charge waves
78A25	电磁理论, 一般理论		Electromagnetic theory, general
78A30	电磁静力学		Electro- and magnetostatics
78A35	带电粒子的运动		Motion of charged particles
78A37	离子阱		Ion traps
78A40	波和辐射		Waves and radiation
78A45	衍射, 散射[WKB方法, 参见34E20]		Diffraction, scattering [See also 34E20 for WKB methods]
78A46	逆散射问题		Inverse scattering problems
78A48	合成介质; 随机介质		Composite media; random media
78A50	天线, 波导		Antennas, wave-guides
78A55	技术应用		Technical applications
78A57	电化学		Electrochemistry
78A60	激光, 微波激射器, 光的双稳性, 非线性光学[参见81V80]		Lasers, masers, optical bistability, nonlinear optics [See also 81V80]
78A70	在生物学上的应用[参见91D30, 92C30]		Biological applications [See also 91D30, 92C30]
78A97	数学上直观推断光学和电磁理论(还必须在这节至少指定一个其它分类号)		Mathematically heuristic optics and electromagnetic theory (must also be assigned at least one other classification number in this section)
78A99	其它		Miscellaneous topics
78Mxx	基本方法		Basic methods
78M05	矩方法		Method of moments
78M10	有限元法		Finite element methods
78M12	有限体积法, 有限积分法		Finite volume methods, finite integration techniques
78M15	边界元法		Boundary element methods
78M16	多极法		Multipole methods
78M20	有限差分法		Finite difference methods
78M22	谱方法		Spectral methods
78M25	其它数值方法		Other numerical methods
78M30	变分法		Variational methods
78M31	Monte Carlo方法		Monte Carlo methods
78M32	神经和启发式方法		Neural and heuristic methods
78M34	模型归约		Model reduction
78M35	渐近分析		Asymptotic analysis
78M40	均匀性		Homogenization
78M50	最优化		Optimization
78M99	其它		None of the above, but in this section
80-XX	经典热力学, 热传导(固体热力学, 见74A15)		Classical thermodynamics, heat transfer (For thermodynamics of solids, see 74A15)
80-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
80-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
80-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
80-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
80-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
80-05	实验论文		Experimental work
80-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
80Axx	热(动)力学和热传导		Thermodynamics and heat transfer
80A05	基础		Foundations
80A10	经典热(动)力学, 包括相对论		Classical thermodynamics, including relativistic
80A17	连续介质热(动)力学[参见74A15]		Thermodynamics of continua [See also 74A15]
80A20	热质量转移, 热流		Heat and mass transfer, heat flow
80A22	Stefan问题、相变等[参见74Nxx]		Stefan problems, phase changes, etc. [See also 74Nxx]
80A23	逆问题		Inverse problems
80A25	燃烧		Combustion
80A30	化学动力学[参见76V05, 92C45, 92E20]		Chemical kinetics [See also 76V05, 92C45, 92E20]
80A32	化学反应流[参见92C45, 92E20]		Chemically reacting flows [See also 92C45, 92E20]
80A50	化学(一般问题)[主要见92Exx]		Chemistry (general) [See mainly 92Exx]
80A99	其它		None of the above, but in this section
80Mxx	基本方法		Basic methods
80M10	有限元法		Finite element methods
80M12	有限体积法		Finite volume methods
80M15	边界元法		Boundary element methods
80M20	有限差分法		Finite difference methods
80M22	谱方法		Spectral methods
80M25	其它数值方法		Other numerical methods
80M30	变分法		Variational methods
80M31	Monte Carlo方法		Monte Carlo methods
80M35	渐近分析		Asymptotic analysis
80M40	均匀性		Homogenization
80M50	最优化		Optimization
80M99	其它		None of the above, but in this section
81-XX	量子理论		Quantum theory
81-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
81-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
81-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
81-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
81-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
81-05	实验论文		Experimental papers
81-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
81-08	计算方法		Computational methods
81Pxx	公理系统, 基础, 哲学		Axiomatics, foundations, philosophy
81P05	一般问题和哲学问题		General and philosophical
81P10	量子力学的逻辑基础; 量子逻辑[参见03G12, 06C15]		Logical foundations of quantum mechanics; quantum logic [See also 03G12, 06C15]
81P13	语境性		Contextuality
81P15	量子测量理论		Quantum measurement theory
81P16	量子态空间, 运算和概率概念		Quantum state spaces, operational and probabilistic concepts
81P20	随机力学(包括随机电动力学)		Stochastic mechanics (including stochastic electrodynamics)
81P40	量子相干性, 纠缠, 量子相关		Quantum coherence, entanglement, quantum correlations
81P45	量子信息, 通讯, 网络[参见94A15, 94A17]		Quantum information, communication, networks [See also 94A15, 94A17]
81P50	量子态估计, 近似克隆		Quantum state estimation, approximate cloning
81P68	量子计算[参见68Q05, 68Q12]		Quantum computation [See also 68Q05, 68Q12]
81P70	量子编码(一般理论)		Quantum coding (general)
81P94	量子密码学[参见94A60]		Quantum cryptography [See also 94A60]
81P99	其它		None of the above, but in this section
81Qxx	量子理论中的一般数学课题和方法		General mathematical topics and methods in quantum theory
81Q05	Schrödinger, Dirac, Klein-Gordon和其它量子力学方程的闭合解和近似解		Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other quantum-mechanical equations
81Q10	量子理论中的自伴算子理论, 包括谱分析		Selfadjoint operator theory in quantum theory, including spectral analysis
81Q12	量子理论中的非自伴算子理论		Non-selfadjoint operator theory in quantum theory
81Q15	算子和微分方程的微扰理论		Perturbation theories for operators and differential equations
81Q20	包括WKB和Maslov方法的半经典技术		Semiclassical techniques including WKB and Maslov methods
81Q30	Feynman积分和Feynman图; 代数拓扑和代数几何的应用[参见14D05, 32S40]		Feynman integrals and graphs; applications of algebraic topology and algebraic geometry [See also 14D05, 32S40]
81Q35	特殊空间: 流形、分形、图等上的量子力学		Quantum mechanics on special spaces: manifolds, fractals, graphs, etc.
81Q37	量子点、波导、ratchets等		Quantum dots, waveguides, ratchets, etc.
81Q40	Bethe-Salpeter和其它积分方程		Bethe-Salpeter and other integral equations
81Q50	量子混沌[参见37Dxx]		Quantum chaos [See also 37Dxx]
81Q60	超对称性和量子力学		Supersymmetry and quantum mechanics
81Q65	alternative量子力学		Alternative quantum mechanics
81Q70	微分-几何(方)法、包括完全相、Berry和Hannay相等		Differential-geometric methods, including holonomy, Berry and Hannay phases, etc.
81Q80	特殊量子系统, 比如: 可解系统		Special quantum systems, such as solvable systems
81Q93	量子控制		Quantum control
81Q99	其它		None of the above, but in this section
81Rxx	量子理论中的群和代数		Groups and algebras in quantum theory
81R05	由物理学诱导的有限维群和代数及其表示[参见20C35, 22E70]		Finite-dimensional groups and algebras motivated by physics and their representations [See also 20C35, 22E70]
81R10	由物理学诱导的无限维群和代数, 包括Virasoro, Kac-Moody, W-代数与其它流行代数及其表示[参见17B65, 17B67, 22E65, 22E67, 22E70]		Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, W-algebras and other current algebras and their representations [See also 17B65, 17B67, 22E65, 22E67, 22E70]
81R12	与可积系统的关系[参见17Bxx, 37J35]		Relations with integrable systems [See also 17Bxx, 37J35]
81R15	算子代数法[参见46Lxx, 81T05]		Operator algebra methods [See also 46Lxx, 81T05]
81R20	协变式波动方程		Covariant wave equations
81R25	旋量和扭子法[参见32L25]		Spinor and twistor methods [See also 32L25]
81R30	相干态[参见22E45]; 压缩态[参见81V80]		Coherent states [See also 22E45]; squeezed states [See also 81V80]
81R40	对称破缺		Symmetry breaking
81R50	量子群和相关代数法[参见16T20, 17B37]		Quantum groups and related algebraic methods [See also 16T20, 17B37]
81R60	非交换几何		Noncommutative geometry
81R99	其它		None of the above, but in this section
81Sxx	一般量子力学和量子化问题		General quantum mechanics and problems of quantization
81S05	正则量子化, 交换关系和统计学		Canonical quantization, commutation relations and statistics
81S10	几何和量子化, 辛方法[参见53D50]		Geometry and quantization, symplectic methods [See also 53D50]
81S20	随机量子化		Stochastic quantization
81S22	开放系统, 约化动力学, 主方程, 去相干[参见82C31]		Open systems, reduced dynamics, master equations, decoherence [See also 82C31]
81S25	量子随机微积分		Quantum stochastic calculus
81S30	包括Wigner分布等的相空间方法		Phase space methods including Wigner distributions, etc.
81S40	路径积分[参见58D30]		Path integrals [See also 58D30]
81S99	其它		None of the above, but in this section
81Txx	量子场论; 相关经典场论[参见70Sxx]		Quantum field theory; related classical field theories [See also 70Sxx]
81T05	公理化量子场论; 算子代数		Axiomatic quantum field theory; operator algebras
81T08	构造量子场论		Constructive quantum field theory
81T10	模型量子场论		Model quantum field theories
81T13	Yang-Mills和其它度规理论[参见53C07, 58E15]		Yang-Mills and other gauge theories [See also 53C07, 58E15]
81T15	重正规化摄动法		Perturbative methods of renormalization
81T16	重正规化非摄动法		Nonperturbative methods of renormalization
81T17	重正规化群方法		Renormalization group methods
81T18	Feynman图解		Feynman diagrams
81T20	弯曲空间上的量子场论		Quantum field theory on curved space backgrounds
81T25	格上的量子场论		Quantum field theory on lattices
81T27	连续统极限		Continuum limits
81T28	热量子场论[参见82B30]		Thermal quantum field theory [See also 82B30]
81T30	弦和超弦理论; 其它广义对象(例如: branes)[参见83E30]		String and superstring theories; other extended objects (e.g., branes) [See also 83E30]
81T40	二维场论、共形场论等		Two-dimensional field theories, conformal field theories, etc.
81T45	拓扑场论[参见57R56, 58Dxx]		Topological field theories [See also 57R56, 58Dxx]
81T50	异常		Anomalies
81T55	Casimir效应		Casimir effect
81T60	超对称场论		Supersymmetric field theories
81T70	场论中的量子化; 上同调方法[参见58D29]		Quantization in field theory; cohomological methods [See also 58D29]
81T75	非交换几何法[参见46L85, 46L87, 58B34]		Noncommutative geometry methods [See also 46L85, 46L87, 58B34]
81T80	模拟和数值建模		Simulation and numerical modeling
81T99	其它		None of the above, but in this section
81Uxx	散射理论[参见34A55, 34L25, 34L40, 35P25, 47A40]		Scattering theory [See also 34A55, 34L25, 34L40, 35P25, 47A40]
81U05	2-体位势散射理论[WKB(方)法参见34E20]		2-body potential scattering theory [See also 34E20 for WKB methods]
81U10	n-体位势散射理论		n-body potential scattering theory
81U15	精确和拟可解系统		Exactly and quasi-solvable systems
81U20	S-矩阵论等		S-matrix theory, etc.
81U30	色散理论, 色散关系		Dispersion theory, dispersion relations
81U35	无弹性和多通道散射		Inelastic and multichannel scattering
81U40	逆散射问题		Inverse scattering problems
81U99	其它		None of the above, but in this section
81Vxx	在特殊物理系统中的应用		Applications to specific physical systems
81V05	强相互作用, 包括量子色动力学		Strong interaction, including quantum chromodynamics
81V10	电磁相互作用; 量子电动力学		Electromagnetic interaction; quantum electrodynamics
81V15	弱相互作用		Weak interaction
81V17	引力相互作用[参见83Cxx和83Exx]		Gravitational interaction [See also 83Cxx and 83Exx]
81V19	其它基本相互作用		Other fundamental interactions
81V22	统一理论		Unified theories
81V25	其它基本粒子理论		Other elementary particle theory
81V35	核物理		Nuclear physics
81V45	原子物理		Atomic physics
81V55	分子物理[参见92E10]		Molecular physics [See also 92E10]
81V65	量子点[参见82D20]		Quantum dots [See also 82D20]
81V70	多体理论; 量子Hall效应		Many-body theory; quantum Hall effect
81V80	量子光学		Quantum optics
81V99	其它		None of the above, but in this section
82-XX	统计力学, 物质结构		Statistical mechanics, structure of matter
82-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
82-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
82-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
82-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
82-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
82-05	实验论文		Experimental papers
82-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
82-08	计算方法		Computational methods
82Bxx	平衡统计力学		Equilibrium statistical mechanics
82B03	基础		Foundations
82B05	经典平衡统计力学(一般问题)		Classical equilibrium statistical mechanics (general)
82B10	量子平衡统计力学(一般问题)		Quantum equilibrium statistical mechanics (general)
82B20	晶格系统(Ising、dimer、Potts等)和图上系统		Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B21	连续统模型(粒子系统等)		Continuum models (systems of particles, etc.)
82B23	精确可解模型; Bethe拟设		Exactly solvable models; Bethe ansatz
82B24	界面问题; 扩散限制聚集		Interface problems; diffusion-limited aggregation
82B26	相变(一般问题)		Phase transitions (general)
82B27	临界现象		Critical phenomena
82B28	重正规化群方法[参见81T17]		Renormalization group methods [See also 81T17]
82B30	统计热动力学[参见80-XX]		Statistical thermodynamics [See also 80-XX]
82B31	随机方法		Stochastic methods
82B35	不可逆热动力学, 包括Onsager-Machlup理论[参见92E20]		Irreversible thermodynamics, including Onsager-Machlup theory [See also 92E20]
82B40	气体动力理论		Kinetic theory of gases
82B41	随机游动、随机表面、晶格animals等[参见60G50, 82C41]		Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
82B43	渗透[参见60K35]		Percolation [See also 60K35]
82B44	无序系统(随机Ising模型、随机Schrödinger算子等)		Disordered systems (random Ising models, random Schrödinger operators, etc.)
82B80	数值方法(Monte Carlo、级数重新求和等)[参见65-XX, 81T80]		Numerical methods (Monte Carlo, series resummation, etc.) [See also 65-XX, 81T80]
82B99	其它		None of the above, but in this section
82Cxx	不定常统计力学(动力学和非平衡)		Time-dependent statistical mechanics (dynamic and nonequilibrium)
82C03	基础		Foundations
82C05	经典动力学和非平衡统计力学(一般问题)		Classical dynamic and nonequilibrium statistical mechanics (general)
82C10	量子动力学和非平衡统计力学(一般问题)		Quantum dynamics and nonequilibrium statistical mechanics (general)
82C20	动力晶格系统(动力学Ising等)和图上系统		Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
82C21	动力连续统模型(粒子系统等)		Dynamic continuum models (systems of particles, etc.)
82C22	交互作用粒子系统[参见60K35]		Interacting particle systems [See also 60K35]
82C23	精确可解动力模型[参见37K60]		Exactly solvable dynamic models [See also 37K60]
82C24	界面问题; 扩散限制聚集		Interface problems; diffusion-limited aggregation
82C26	动力学和非平衡相变(一般问题)		Dynamic and nonequilibrium phase transitions (general)
82C27	动力学临界现象		Dynamic critical phenomena
82C28	动力学重正规化群方法[参见81T17]		Dynamic renormalization group methods [See also 81T17]
82C31	随机方法(Fokker-Planck、Langevin等)[参见60H10]		Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
82C32	神经网[参见68T05, 91E40, 92B20]		Neural nets [See also 68T05, 91E40, 92B20]
82C35	不可逆热动力学, 包括Onsager-Machlup理论		Irreversible thermodynamics, including Onsager-Machlup theory
82C40	气体动力理论		Kinetic theory of gases
82C41	随机游动、随机表面、晶格animals等的动力学[参见60G50]		Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]
82C43	不定常渗透[参见60K35]		Time-dependent percolation [See also 60K35]
82C44	无序系统(随机Ising系统等)的动力学		Dynamics of disordered systems (random Ising systems, etc.)
82C70	输运过程		Transport processes
82C80	数值方法(Monte Carlo、级数重新求和等)		Numerical methods (Monte Carlo, series resummation, etc.)
82C99	其它		None of the above, but in this section
82Dxx	在特殊类型物理系统中的应用		Applications to specific types of physical systems
82D05	气体		Gases
82D10	等离子体		Plasmas
82D15	液体		Liquids
82D20	固体		Solids
82D25	晶体(结晶群理论, 见20H15)		Crystals (For crystallographic group theory, see 20H15)
82D30	随机介质, 无序材料(包括液晶和自旋玻璃)		Random media, disordered materials (including liquid crystals and spin glasses)
82D35	金属		Metals
82D37	半导体		Semiconductors
82D40	磁性材料		Magnetic materials
82D45	铁电体		Ferroelectrics
82D50	超流体		Superfluids
82D55	超导体		Superconductors
82D60	聚合物		Polymers
82D75	核反应堆理论; 中子输运		Nuclear reactor theory; neutron transport
82D77	量子波导, 量子线[参见78A50]		Quantum wave guides, quantum wires [See also 78A50]
82D80	纳米结构和纳米粒子		Nanostructures and nanoparticles
82D99	其它		None of the above, but in this section
83-XX	相对论和引力理论		Relativity and gravitational theory
83-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
83-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
83-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
83-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
83-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
83-05	实验工作		Experimental work
83-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
83-08	计算方法		Computational methods
83Axx	狭义相对论		Special relativity
83A05	狭义相对论		Special relativity
83A99	其它		None of the above, but in this section
83Bxx	观测问题和实验问题		Observational and experimental questions
83B05	观测问题和实验问题		Observational and experimental questions
83B99	其它		None of the above, but in this section
83Cxx	广义相对论		General relativity
83C05	Einstein方程(一般结构, 正则形式, Cauchy问题)		Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C10	运动方程		Equations of motion
83C15	精确解		Exact solutions
83C20	解的种类; 代数特殊解, 对称度量		Classes of solutions; algebraically special solutions, metrics with symmetries
83C22	Einstein-Maxwell方程		Einstein-Maxwell equations
83C25	近似方法, 弱场		Approximation procedures, weak fields
83C27	晶格引力, Regge微积分与其它离散方法		Lattice gravity, Regge calculus and other discrete methods
83C30	渐近(方)法(辐射、新函数、H-空间等)		Asymptotic procedures (radiation, news functions, H-spaces, etc.)
83C35	引力波		Gravitational waves
83C40	引力能量和守恒律; 运动群		Gravitational energy and conservation laws; groups of motions
83C45	引力场的量子化		Quantization of the gravitational field
83C47	量子场论方法[参见81T20]		Methods of quantum field theory [See also 81T20]
83C50	电磁场		Electromagnetic fields
83C55	引力场同物质(流体动力学等)的宏观相互作用		Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C57	黑洞		Black holes
83C60	旋量和扭子法; Newman-Penrose形式		Spinor and twistor methods; Newman-Penrose formalism
83C65	非交换几何方法[参见58B34]		Methods of noncommutative geometry [See also 58B34]
83C75	时空奇异性、宇宙的督察等		Space-time singularities, cosmic censorship, etc.
83C80	低维中的模拟		Analogues in lower dimensions
83C99	其它		None of the above, but in this section
83Dxx	非Einstein相对引力理论, 包括非对称场论		Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83D05	非Einstein相对引力理论, 包括非对称场论		Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83D99	其它		None of the above, but in this section
83Exx	统一场论, 高维场论和超场论		Unified, higher-dimensional and super field theories
83E05	几何动力学		Geometrodynamics
83E15	Kaluza-Klein和其它高维理论		Kaluza-Klein and other higher-dimensional theories
83E30	弦和超弦理论[参见81T30]		String and superstring theories [See also 81T30]
83E50	超引力		Supergravity
83E99	其它		None of the above, but in this section
83Fxx	宇宙论		Cosmology
83F05	宇宙论		Cosmology
83F99	其它		None of the above, but in this section
85-XX	天文学和天体物理学(天体力学, 见70F15)		Astronomy and astrophysics (For celestial mechanics, see 70F15)
85-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
85-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
85-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
85-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
85-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
85-05	实验工作		Experimental work
85-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
85-08	计算方法		Computational methods
85Axx	天文学和天体物理学(天体力学, 见70F15)		Astronomy and astrophysics (For celestial mechanics, see 70F15)
85A04	一般问题		General
85A05	银河系和天体动力学		Galactic and stellar dynamics
85A15	银河系和天体结构		Galactic and stellar structure
85A20	行星大气		Planetary atmospheres
85A25	辐射传导		Radiative transfer
85A30	流体动力问题和流体磁力问题[参见76Y05]		Hydrodynamic and hydromagnetic problems [See also 76Y05]
85A35	统计天文学		Statistical astronomy
85A40	宇宙学(相对论的宇宙学, 见83F05)		Cosmology (For relativistic cosmology, see 83F05)
85A99	各种课题		Miscellaneous topics
86-XX	地球物理学[参见76U05, 76V05]		Geophysics [See also 76U05, 76V05]
86-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
86-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
86-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
86-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
86-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
86-05	实验工作		Experimental work
86-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
86-08	计算方法		Computational methods
86Axx	地球物理学[参见76U05, 76V05]		Geophysics [See also 76U05, 76V05]
86A04	一般问题		General
86A05	水文学, 水文地理学, 海洋学[参见76Bxx, 76E20, 76Q05, 76Rxx, 76U05]		Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]
86A10	气象学和大气物理学[参见76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]		Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]
86A15	地震学		Seismology
86A17	地球动力学, 地震问题		Global dynamics, earthquake problems
86A20	位势, 勘探		Potentials, prospecting
86A22	逆问题[参见35R30]		Inverse problems [See also 35R30]
86A25	地电学和地磁学[参见76W05, 78A25]		Geo-electricity and geomagnetism [See also 76W05, 78A25]
86A30	大地测量学, 绘图问题		Geodesy, mapping problems
86A32	大地统计学		Geostatistics
86A40	冰川学		Glaciology
86A60	地质问题		Geological problems
86A99	各种课题		Miscellaneous topics
90-XX	运筹学, 数学规划		Operations research, mathematical programming
90-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
90-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
90-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
90-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
90-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
90-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
90-08	计算方法		Computational methods
90Bxx	运筹学和管理科学		Operations research and management science
90B05	库存, 存储, 储藏所		Inventory, storage, reservoirs
90B06	运输, 物流		Transportation, logistics
90B10	网络模型, 确定的		Network models, deterministic
90B15	网络模型, 随机的		Network models, stochastic
90B18	通信网络[参见68M10, 94A05]		Communication networks [See also 68M10, 94A05]
90B20	交通问题		Traffic problems
90B22	排队和服务[参见60K25, 68M20]		Queues and service [See also 60K25, 68M20]
90B25	可靠性, 有效性, 维修, 检查[参见60K10, 62N05]		Reliability, availability, maintenance, inspection [See also 60K10, 62N05]
90B30	生产模型		Production models
90B35	调度理论, 确定的[参见68M20]		Scheduling theory, deterministic [See also 68M20]
90B36	调度理论, 随机的[参见68M20]		Scheduling theory, stochastic [See also 68M20]
90B40	搜索理论		Search theory
90B50	管理决策, 包括多目标[参见90C29, 90C31, 91A35, 91B06]		Management decision making, including multiple objectives [See also 90C29, 90C31, 91A35, 91B06]
90B60	市场营销, 广告[参见91B60]		Marketing, advertising [See also 91B60]
90B70	组织理论, 人力计划的理论[参见91D35]		Theory of organizations, manpower planning [See also 91D35]
90B80	分散选址和分配[参见90C10]		Discrete location and assignment [See also 90C10]
90B85	连续选址		Continuous location
90B90	面向案例研究		Case-oriented studies
90B99	其它		None of the above, but in this section
90Cxx	数学规划[参见49Mxx, 65Kxx]		Mathematical programming [See also 49Mxx, 65Kxx]
90C05	线性规划		Linear programming
90C06	大规模问题		Large-scale problems
90C08	线性规划的特殊问题(运输、多指标等)		Special problems of linear programming (transportation, multi-index, etc.)
90C09	Boole规划		Boolean programming
90C10	整数规划		Integer programming
90C11	混合整数规划		Mixed integer programming
90C15	随机规划		Stochastic programming
90C20	二次规划		Quadratic programming
90C22	半定规划		Semidefinite programming
90C25	凸规划		Convex programming
90C26	非凸规划, 全局最优化		Nonconvex programming, global optimization
90C27	组合最优化		Combinatorial optimization
90C29	多目标规划和目标规划		Multi-objective and goal programming
90C30	非线性规划		Nonlinear programming
90C31	灵敏度, 稳定性, 参量最优化		Sensitivity, stability, parametric optimization
90C32	分式规划		Fractional programming
90C33	互补性, 均衡问题和变分不等式(有限维)		Complementarity and equilibrium problems and variational inequalities (finite dimensions)
90C34	半无限规划		Semi-infinite programming
90C35	涉及图或网络的规划[参见90C27]		Programming involving graphs or networks [See also 90C27]
90C39	动态规划[参见49L20]		Dynamic programming [See also 49L20]
90C40	Markov和半Markov决策过程		Markov and semi-Markov decision processes
90C46	最优化条件, 对偶性[参见49N15]		Optimality conditions, duality [See also 49N15]
90C47	极小极大问题[参见49K35]		Minimax problems [See also 49K35]
90C48	抽象空间中的规划		Programming in abstract spaces
90C49	极值点和旋转方法		Extreme-point and pivoting methods
90C51	内点法		Interior-point methods
90C52	既约梯度型方法		Methods of reduced gradient type
90C53	拟Newton型方法		Methods of quasi-Newton type
90C55	逐次二次规划型方法		Methods of successive quadratic programming type
90C56	无导数法和使用广义导数的方法[参见49J52]		Derivative-free methods and methods using generalized derivatives [See also 49J52]
90C57	多面体组合学, 分枝定界, 分枝切割		Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C59	近似法和启发式		Approximation methods and heuristics
90C60	数学规划问题的抽象计算复杂性[参见68Q25]		Abstract computational complexity for mathematical programming problems [See also 68Q25]
90C70	模糊规划		Fuzzy programming
90C90	数学规划的应用		Applications of mathematical programming
90C99	其它		None of the above, but in this section
91-XX	对策论, 经济学, 社会科学和行为科学		Game theory, economics, social and behavioral sciences
91-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
91-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
91-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
91-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from section 01)
91-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
91-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
91-08	计算方法		Computational methods
91Axx	对策论		Game theory
91A05	2-人对策		2-person games
91A06	n-人对策, n >2		n-person games, n >2
91A10	非合作对策		Noncooperative games
91A12	合作对策		Cooperative games
91A13	无穷多局中人对策		Games with infinitely many players
91A15	随机对策		Stochastic games
91A18	扩展型对策		Games in extensive form
91A20	多级对策和重复对策		Multistage and repeated games
91A22	进化对策		Evolutionary games
91A23	微分对策[参见49N70]		Differential games [See also 49N70]
91A24	位置对策(追逃对策等)[参见49N75]		Positional games (pursuit and evasion, etc.) [See also 49N75]
91A25	动态对策		Dynamic games
91A26	推理, 学习		Rationality, learning
91A28	信号, 通信		Signaling, communication
91A30	对策的效用理论[参见91B16]		Utility theory for games [See also 91B16]
91A35	对策的决策理论[参见62Cxx, 91B06, 91B50]		Decision theory for games [See also 62Cxx, 91B06, 90B50]
91A40	对策论模型		Game-theoretic models
91A43	包括图的对策[参见05C57]		Games involving graphs [See also 05C57]
91A44	包括拓扑或集论的对策		Games involving topology or set theory
91A46	组合对策		Combinatorial games
91A50	离散时间对策		Discrete-time games
91A55	定时对策		Games of timing
91A60	概率对策; 赌博[参见60G40]		Probabilistic games; gambling [See also 60G40]
91A65	层次对策		Hierarchical games
91A70	对策空间		Spaces of games
91A80	对策论的应用		Applications of game theory
91A90	实验研究		Experimental studies
91A99	其它		None of the above, but in this section
91Bxx	数理经济学(计量经济学, 见62P20)		Mathematical economics (For econometrics, see 62P20)
91B02	基础课题(基础数学, 方法论; 一般应用于经济)		Fundamental topics (basic mathematics, methodology; applicable to economics in general)
91B06	决策理论[参见62Cxx, 90B50, 91A35]		Decision theory [See also 62Cxx, 90B50, 91A35]
91B08	个体选择		Individual preferences
91B10	团体选择		Group preferences
91B12	表决理论		Voting theory
91B14	社会选择		Social choice
91B15	福利经济学		Welfare economics
91B16	效用理论		Utility theory
91B18	公共财产		Public goods
91B24	价格理论和市场结构		Price theory and market structure
91B25	资产定价模型		Asset pricing models
91B26	市场模型(拍卖、议价、出价、销售等)		Market models (auctions, bargaining, bidding, selling, etc.)
91B30	风险理论, 保险		Risk theory, insurance
91B32	资源和费用分配		Resource and cost allocation
91B38	生产理论, 企业理论		Production theory, theory of the firm
91B40	劳动市场, 合同		Labor market, contracts
91B42	消费行为, 需求理论		Consumer behavior, demand theory
91B44	信息经济学		Informational economics
91B50	一般均衡理论		General equilibrium theory
91B51	动态随机一般均衡理论		Dynamic stochastic general equilibrium theory
91B52	特殊均衡类型		Special types of equilibria
91B54	特殊经济类型		Special types of economies
91B55	经济动态学		Economic dynamics
91B60	贸易模型		Trade models
91B62	成长模型		Growth models
91B64	宏观经济模型(货币模型, 税收模型)		Macro-economic models (monetary models, models of taxation)
91B66	多部门模型		Multisectoral models
91B68	匹配模型		Matching models
91B69	异构主体模型		Heterogeneous agent models
91B70	随机模型		Stochastic models
91B72	空间模型		Spatial models
91B74	真实世界系统模型		Models of real-world systems
91B76	环境经济学(天然资源模型、收成、污染等)		Environmental economics (natural resource models, harvesting, pollution, etc.)
91B80	统计学和量子力学在经济学(经济物理学)的应用		Applications of statistical and quantum mechanics to economics (econophysics)
91B82	统计方法; 经济指标和经济度量		Statistical methods; economic indices and measures
91B84	经济时间序列分析[参见62M10]		Economic time series analysis [See also 62M10]
91B99	其它		None of the above, but in this section
91Cxx	社会科学和行为科学: 一般课题(统计学, 见62-XX)		Social and behavioral sciences: general topics (For statistics, see 62-XX)
91C05	测量理论		Measurement theory
91C15	一维和多维定标		One- and multidimensional scaling
91C20	聚类[参见62H30]		Clustering [See also 62H30]
91C99	其它		None of the above, but in this section
91Dxx	数理社会学(包括人类学)		Mathematical sociology (including anthropology)
91D10	社会学, 社会和城市发展模型		Models of societies, social and urban evolution
91D20	数学地理学和数学人口统计学		Mathematical geography and demography
91D25	空间模型[参见91B72]		Spatial models [See also 91B72]
91D30	社会网络		Social networks
91D35	人力系统[参见91B40, 90B70]		Manpower systems [See also 91B40, 90B70]
91D99	其它		None of the above, but in this section
91Exx	数理心理学		Mathematical psychology
91E10	认识心理学		Cognitive psychology
91E30	心理物理学和心理生理学; 感觉		Psychophysics and psychophysiology; perception
91E40	记忆和学习[参见68T05]		Memory and learning [See also 68T05]
91E45	测量与性能		Measurement and performance
91E99	其它		None of the above, but in this section
91Fxx	其它社会科学和行为科学(数学处理)		Other social and behavioral sciences (mathematical treatment)
91F10	历史学, 政治学		History, political science
91F20	语言学[参见03B65, 68T50]		Linguistics [See also 03B65, 68T50]
91F99	其它		None of the above, but in this section
91Gxx	数理金融学		Mathematical finance
91G10	投资组合理论		Portfolio theory
91G20	衍生证券		Derivative securities
91G30	银行利率(随机模型)		Interest rates (stochastic models)
91G40	信贷风险		Credit risk
91G50	公司理财		Corporate finance
91G60	数值方法(包括Monte Carlo方法)		Numerical methods (including Monte Carlo methods)
91G70	统计方法, 计量经济学		Statistical methods, econometrics
91G80	其它理论的金融应用(随机控制, 变分法, 偏微分方程, 随机偏微分方程, 动力系统)		Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
91G99	其它		None of the above, but in this section
92-XX	生物学和其它自然科学		Biology and other natural sciences
92-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
92-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
92-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
92-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
92-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
92-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
92-08	计算方法		Computational methods
92Bxx	一般数学生物学		Mathematical biology in general
92B05	一般生物学和生物数学		General biology and biomathematics
92B10	分类学, 统计		Taxonomy, statistics
92B15	一般生物统计学[参见62P10]		General biostatistics [See also 62P10]
92B20	神经网络, 人工生命和相关课题[参见68T05, 82C32, 94Cxx]		Neural networks, artificial life and related topics [See also 68T05, 82C32, 94Cxx]
92B25	生物节律与同步现象		Biological rhythms and synchronization
92B99	其它		None of the above, but in this section
92Cxx	生理学, 细胞和医学课题		Physiological, cellular and medical topics
92C05	生物物理学		Biophysics
92C10	生物力学[参见74L15]		Biomechanics [See also 74L15]
92C15	发生生物学, 模式结构		Developmental biology, pattern formation
92C17	细胞运动(趋药性等)		Cell movement (chemotaxis, etc.)
92C20	神经生物学		Neural biology
92C30	生理学(一般问题)		Physiology (general)
92C35	生理学流[参见76Z05]		Physiological flow [See also 76Z05]
92C37	细胞生物学		Cell biology
92C40	生物化学, 分子生物学		Biochemistry, molecular biology
92C42	系统生物学, 网络		Systems biology, networks
92C45	生物化学问题中的动力学(药物动力学、酶动力学等)[参见80A30]		Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30]
92C50	药学应用(一般问题)		Medical applications (general)
92C55	生物医学图象和信号处理[参见44A12, 65R10]		Biomedical imaging and signal processing [See also 44A12, 65R10]
92C60	医学流行病学		Medical epidemiology
92C80	作物生物学		Plant biology
92C99	其它		None of the above, but in this section
92Dxx	遗传学和种群动力学		Genetics and population dynamics
92D10	遗传学(遗传代数, 见17D92)		Genetics (For genetic algebras, see 17D92)
92D15	与进化有关的问题		Problems related to evolution
92D20	蛋白质序列, DNA序列		Protein sequences, DNA sequences
92D25	种群动力学(一般问题)		Population dynamics (general)
92D30	流行病学		Epidemiology
92D40	生态学		Ecology
92D50	动物行为		Animal behavior
92D99	其它		None of the above, but in this section
92Exx	化学(生物化学, 见92C40)		Chemistry (For biochemistry, see 92C40)
92E10	分子结构(图论方法、微分拓扑方法等)		Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
92E20	经典流、经典反应等[参见80A30, 80A32]		Classical flows, reactions, etc. [See also 80A30, 80A32]
92E99	其它		None of the above, but in this section
92Fxx	其它自然科学(还必须在92-XX中至少指定一个分类号)		Other natural sciences (should also be assigned at least one other classification number in this section)
92F05	其它自然科学(还必须在92-XX中至少指定一个分类号)		Other natural sciences (should also be assigned at least one other classification number in section 92)
92F99	其它		None of the above, but in this section
93-XX	系统论; 控制(最优控制, 见49-XX)		Systems theory; control (For optimal control, see 49-XX)
93-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
93-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
93-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
93-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
93-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
93-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
93Axx	一般理论		General
93A05	公理系统理论		Axiomatic system theory
93A10	一般系统		General systems
93A13	等级系统		Hierarchical systems
93A14	分散系统		Decentralized systems
93A15	大规模系统		Large scale systems
93A30	数学模型建立(系统模型、模型匹配等)		Mathematical modeling (models of systems, model-matching, etc.)
93A99	其它		None of the above, but in this section
93Bxx	可控性, 可观测性和系统结构		Controllability, observability, and system structure
93B03	可达集		Attainable sets
93B05	可控性		Controllability
93B07	可观测性		Observability
93B10	标准结构		Canonical structure
93B11	系统结构简化		System structure simplification
93B12	变量结构系统		Variable structure systems
93B15	输入-输出数据的实现		Realizations from input-output data
93B17	变换		Transformations
93B18	线性化		Linearizations
93B20	极小系统表示		Minimal systems representations
93B25	代数方法		Algebraic methods
93B27	几何方法		Geometric methods
93B28	算子理论方法[参见47A48, 47A57, 47B35, 47N70]		Operator-theoretic methods [See also 47A48, 47A57, 47B35, 47N70]
93B30	系统辨识		System identification
93B35	灵敏度(鲁棒性)		Sensitivity (robustness)
93B36	H^∞-控制		H^∞-control
93B40	计算方法		Computational methods
93B50	综合问题		Synthesis problems
93B51	设计技术(鲁棒设计、计算机辅助设计等)		Design techniques (robust design, computer-aided design, etc.)
93B52	反馈控制		Feedback control
93B55	极点和零点配置问题		Pole and zero placement problems
93B60	特征值问题		Eigenvalue problems
93B99	其它		None of the above, but in this section
93Cxx	控制系统		Control systems
93C05	线性系统		Linear systems
93C10	非线性系统		Nonlinear systems
93C15	常微分方程控制系统[参见34H05]		Systems governed by ordinary differential equations [See also 34H05]
93C20	偏微分方程控制系统		Systems governed by partial differential equations
93C23	泛函-微分方程控制系统[参见34K35]		Systems governed by functional-differential equations [See also 34K35]
93C25	抽象空间中的系统		Systems in abstract spaces
93C30	函数关系而不是微分方程的控制系统(像混合与开关系统)		Systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C35	多变量系统		Multivariable systems
93C40	自适应控制		Adaptive control
93C41	不完全信息问题		Problems with incomplete information
93C42	模糊控制系统		Fuzzy control systems
93C55	离散时间系统		Discrete-time systems
93C57	抽样数据系统		Sampled-data systems
93C62	数字系统		Digital systems
93C65	离散事件系统		Discrete event systems
93C70	时标分析和奇异摄动		Time-scale analysis and singular perturbations
93C73	摄动		Perturbations
93C80	频率响应方法		Frequency-response methods
93C83	包括计算机的控制问题(过程控制等)		Control problems involving computers (process control, etc.)
93C85	自动系统(机器人等)[参见68T40, 70B15, 70Q05]		Automated systems (robots, etc.) [See also 68T40, 70B15, 70Q05]
93C95	应用		Applications
93C99	其它		None of the above, but in this section
93Dxx	稳定性		Stability
93D05	Lyapunov和其它经典稳定性(Lagrange、Poisson、L^p、 l^p等)		Lyapunov and other classical stabilities (Lagrange, Poisson, L^p, l^p, etc.)
93D09	鲁棒稳定性		Robust stability
93D10	反馈系统的Popov型稳定性		Popov-type stability of feedback systems
93D15	反馈系统的稳定化		Stabilization of systems by feedback
93D20	渐近稳定性		Asymptotic stability
93D21	自适应或鲁棒稳定化		Adaptive or robust stabilization
93D25	输入-输出方法		Input-output approaches
93D30	标量和向量Lyapunov函数		Scalar and vector Lyapunov functions
93D99	其它		None of the above, but in this section
93Exx	随机系统和控制		Stochastic systems and control
93E03	随机系统, 一般问题		Stochastic systems, general
93E10	估计和检测[参见60G35]		Estimation and detection [See also 60G35]
93E11	滤波[参见60G35]		Filtering [See also 60G35]
93E12	系统辨识		System identification
93E14	数据修匀		Data smoothing
93E15	随机稳定性		Stochastic stability
93E20	最优随机控制		Optimal stochastic control
93E24	最小二乘法和相关方法		Least squares and related methods
93E25	其它计算方法		Other computational methods
93E35	随机学习和自适应控制		Stochastic learning and adaptive control
93E99	其它		None of the above, but in this section
94-XX	信息和通讯, 电路		Information and communication, circuits
94-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
94-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
94-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
94-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
94-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
94-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
94Axx	通讯, 信息		Communication, information
94A05	通讯理论[参见60G35, 90B18]		Communication theory [See also 60G35, 90B18]
94A08	图象处理(压缩、重构等)[参见68U10]		Image processing (compression, reconstruction, etc.) [See also 68U10]
94A11	正交和其它特殊函数的应用		Application of orthogonal and other special functions
94A12	信号理论(特征、重构、滤波等)		Signal theory (characterization, reconstruction, filtering, etc.)
94A13	检测理论		Detection theory
94A14	调幅和解调		Modulation and demodulation
94A15	信息理论, 一般问题[参见62B10, 81P94]		Information theory, general [See also 62B10, 81P94]
94A17	信息测度, 熵		Measures of information, entropy
94A20	抽样理论		Sampling theory
94A24	编码定理(香农理论)		Coding theorems (Shannon theory)
94A29	源编码[参见68P30]		Source coding [See also 68P30]
94A34	速率畸变理论		Rate-distortion theory
94A40	信道模型(包括量子)		Channel models (including quantum)
94A45	前缀码, 长度可变码, 无逗号码[参见20M35, 68Q45]		Prefix, length-variable, comma-free codes [See also 20M35, 68Q45]
94A50	调查表理论		Theory of questionnaires
94A55	移位寄存器序列和有限alphabets序列		Shift register sequences and sequences over finite alphabets
94A60	密码术[参见11T71, 14G50, 68P25, 81P94]		Cryptography [See also 11T71, 14G50, 68P25, 81P94]
94A62	鉴别和秘密共享[参见81P94]		Authentication and secret sharing [See also 81P94]
94A99	其它		None of the above, but in this section
94Bxx	误差校正码和误差检测码理论		Theory of error-correcting codes and error-detecting codes
94B05	线性码, 一般问题		Linear codes, general
94B10	卷积码		Convolutional codes
94B12	组合调幅方案(包括格子结构码)		Combined modulation schemes (including trellis codes)
94B15	循环码		Cyclic codes
94B20	段校正码		Burst-correcting codes
94B25	组合码		Combinatorial codes
94B27	几何方法(包括代数几何的应用)[参见11T71, 14G50]		Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]
94B30	主码		Majority codes
94B35	译码		Decoding
94B40	算术码[参见11T71, 14G50]		Arithmetic codes [See also 11T71, 14G50]
94B50	同步误差校正码		Synchronization error-correcting codes
94B60	其它类型码		Other types of codes
94B65	编码范围		Bounds on codes
94B70	误差概率		Error probability
94B75	凸集理论的应用和数的几何(覆盖半径等)[参见11H31]		Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) [See also 11H31]
94B99	其它		None of the above, but in this section
94Cxx	电路, 网络		Circuits, networks
94C05	解析电路理论		Analytic circuit theory
94C10	开关理论, Boole代数的应用; Boole函数[参见06E30]		Switching theory, application of Boolean algebra; Boolean functions [See also 06E30]
94C12	故障检测; 测试		Fault detection; testing
94C15	图论的应用[参见05Cxx, 68R10]		Applications of graph theory [See also 05Cxx, 68R10]
94C30	设计理论的应用[参见05Bxx]		Applications of design theory [See also 05Bxx]
94C99	其它		None of the above, but in this section
94Dxx	模糊集和模糊逻辑(与94部分的问题有关)[参见03B52, 03E72, 28E10]		Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]
94D05	模糊集和模糊逻辑(与94-XX的问题有关)[参见03B52, 03E72, 28E10]		Fuzzy sets and logic (in connection with questions of Section 94) [See also 03B52, 03E72, 28E10]
94D99	其它		None of the above, but in this section
97-XX	数学教育		Mathematics education
97-00	一般参考书(手册、辞典、书目等)		General reference works (handbooks, dictionaries, bibliographies, etc.)
97-01	教学阐述(教科书、教学论文等)		Instructional exposition (textbooks, tutorial papers, etc.)
97-02	研究阐述(专著, 评述论文)		Research exposition (monographs, survey articles)
97-03	历史(还必须在01-XX中至少指定一个分类号)		Historical (must also be assigned at least one classification number from Section 01)
97-04	明显的机器计算和程序(非计算或程序设计理论)		Explicit machine computation and programs (not the theory of computation or programming)
97-06	会议录、会议、文集等		Proceedings, conferences, collections, etc.
97Axx	一般理论, 数学与教育		General, mathematics and education
97A10	综合作品, 参考书		Comprehensive works, reference books
97A20	娱乐数学, 游戏[参见00A08]		Recreational mathematics, games [See also 00A08]
97A30	数学与数学教育的历史[参见01-XX]		History of mathematics and mathematics education [See also 01-XX]
97A40	数学与社会		Mathematics and society
97A50	参考书目[参见01-00]		Bibliographies [See also 01-00]
97A70	论文与博士后论文		Theses and postdoctoral these
97A80	数学的普及		Popularization of mathematics
97A99	其它		None of the above, but in this section
97Bxx	教育政策和教育系统		Educational policy and educational systems
97B10	教育研究和教育计划		Educational research and planning
97B20	普通教育		General education
97B30	职业教育		Vocational education
97B40	高等教育		Higher education
97B50	教师进修(研究方面, 见97C70)		Teacher education (For research aspects, see 97C70)
97B60	成人和继续教育		Adult and further education
97B70	教学大纲, 教育标准		Syllabuses, educational standards
97B99	其它		None of the above, but in this section
97Cxx	数学教育心理学和数学教育研究		Psychology of and research in mathematics education
97C10	综合作品		Comprehensive works
97C20	情感行为		Affective behavior
97C30	认知过程, 学习理论		Cognitive processes, learning theories
97C40	智力和才能		Intelligence and aptitudes
97C50	语言和口头交流		Language and verbal communication
97C60	学习的社会学方面		Sociological aspects of learning
97C70	教学过程		Teaching-learning processes
97C99	其它		None of the above, but in this section
97Dxx	数学教育和说明		Education and instruction in mathematics
97D10	综合作品, 比较研究		Comprehensive works, comparative studies
97D20	哲学和理论贡献(数学教学法)		Philosophical and theoretical contributions (maths didactics)
97D30	目标和目的		Objectives and goals
97D40	教学法和课堂技巧		Teaching methods and classroom techniques
97D50	教学问题的解决和启发式策略(研究方面, 见97Cxx)		Teaching problem solving and heuristic strategies (For research aspects, see 97Cxx)
97D60	学生评估, 成绩控制和评定		Student assessment, achievement control and rating
97D70	学习难点和学生错误		Learning difficulties and student errors
97D80	教育机构和草拟课程		Teaching units and draft lessons
97D99	其它		None of the above, but in this section
97Exx	数学基础		Foundations of mathematics
97E10	综合作品		Comprehensive works
97E20	哲学和数学		Philosophy and mathematics
97E30	逻辑		Logic
97E40	数学语言		Language of mathematics
97E50	数学课堂上的推理与证明		Reasoning and proving in the mathematics classroom
97E60	集合, 关系, 集合论		Sets, relations, set theory
97E99	其它		None of the above, but in this section
97Fxx	算术, 数论		Arithmetic, number theory
97F10	综合作品		Comprehensive works
97F20	准数阶段, 数的概念		Pre-numerical stage, concept of numbers
97F30	自然数		Natural numbers
97F40	整数, 有理数		Integers, rational numbers
97F50	实数, 复数		Real numbers, complex numbers
97F60	数论		Number theory
97F70	测度与单位		Measures and units
97F80	比率和比例, 百分数		Ratio and proportion, percentages
97F90	现实生活中的数学, 实用算术		Real life mathematics, practical arithmetic
97F99	其它		None of the above, but in this section
97Gxx	几何		Geometry
97G10	综合作品		Comprehensive works
97G20	非形式几何		Informal geometry
97G30	面积和体积		Areas and volumes
97G40	平面和立体几何		Plane and solid geometry
97G50	变换几何		Transformation geometry
97G60	平面和球面三角学		Plane and spherical trigonometry
97G70	解析几何, 向量代数		Analytic geometry. Vector algebra
97G80	画法几何		Descriptive geometry
97G99	其它		None of the above, but in this section
97Hxx	代数		Algebra
97H10	综合作品		Comprehensive works
97H20	初级代数		Elementary algebra
97H30	方程和不等式		Equations and inequalities
97H40	群, 环, 域		Groups, rings, fields
97H50	有序代数结构		Ordered algebraic structures
97H60	线性代数		Linear algebra
97H99	其它		None of the above, but in this section
97Ixx	分析		Analysis
97I10	综合作品		Comprehensive works
97I20	映射和函数		Mappings and functions
97I30	序列和级数		Sequences and series
97I40	微分学		Differential calculus
97I50	积分学		Integral calculus
97I60	多变量函数		Functions of several variables
97I70	泛函方程		Functional equations
97I80	复分析		Complex analysis
97I99	其它		None of the above, but in this section
97Kxx	组合学, 图论, 概率论, 统计学		Combinatorics, graph theory, probability theory, statistics
97K10	综合作品		Comprehensive works
97K20	组合学		Combinatorics
97K30	图论		Graph theory
97K40	描述统计学		Descriptive statistics
97K50	概率论		Probability theory
97K60	分布与随机过程		Distributions and stochastic processes
97K70	统计学的基础和方法论		Foundations and methodology of statistics
97K80	应用统计学		Applied statistics
97K99	其它		None of the above, but in this section
97Mxx	数学建模, 数学的应用		Mathematical modeling, applications of mathematics
97M10	建模与交叉学科		Modeling and interdisciplinarity
97M20	职业训练和职业教育中的数学		Mathematics in vocational training and career education
97M30	金融和保险数学		Financial and insurance mathematics
97M40	运筹学, 经济学		Operations research, economics
97M50	物理学, 天文学, 技术, 工程		Physics, astronomy, technology, engineering
97M60	生物学, 化学, 医学		Biology, chemistry, medicine
97M70	行为和社会科学		Behavioral and social sciences
97M80	艺术, 音乐, 语言, 建筑学		Arts, music, language, architecture
97M99	其它		None of the above, but in this section
97Nxx	数值数学		Numerical mathematics
97N10	综合作品		Comprehensive works
97N20	误差的舍入, 估计, 理论		Rounding, estimation, theory of errors
97N30	数值代数		Numerical algebra
97N40	数值分析		Numerical analysis
97N50	插值与逼近		Interpolation and approximation
97N60	数学规划		Mathematical programming
97N70	离散数学		Discrete mathematics
97N80	数学软件, 计算机程序		Mathematical software, computer programs
97N99	其它		None of the above, but in this section
97Pxx	计算机科学		Computer science
97P10	综合作品		Comprehensive works
97P20	计算机科学理论		Theory of computer science
97P30	系统软件		System software
97P40	程序设计语言		Programming languages
97P50	程序设计技术		Programming techniques
97P60	硬件		Hardware
97P70	计算机科学与社会		Computer science and society
97P99	其它		None of the above, but in this section
97Qxx	计算机科学教育		Computer science education
97Q10	综合作品		Comprehensive works
97Q20	计算机科学教学中的情感因素		Affective aspects in teaching computer science
97Q30	认知过程		Cognitive processes
97Q40	社会学方面		Sociological aspects
97Q50	目标		Objectives
97Q60	教学方法和课堂教学技巧		Teaching methods and classroom techniques
97Q70	学生评价		Student assessment
97Q80	教学单位		Teaching units
97Q99	其它		None of the above, but in this section
97Rxx	计算机科学应用		Computer science applications
97R10	综合作品, 程序集		Comprehensive works, collections of programs
97R20	在数学中的应用		Applications in mathematics
97R30	在科学中的应用		Applications in sciences
97R40	人工智能		Artificial intelligence
97R50	数据库, 信息系统		Data bases, information systems
97R60	计算机图形学		Computer graphics
97R70	用户程序, 管理应用		User programs, administrative applications
97R80	娱乐计算		Recreational computing
97R99	其它		None of the above, but in this section
97Uxx	教材和(多)媒体, 教育技术		Educational material and media, educational technology
97U10	综合作品		Comprehensive works
97U20	教科书.教科书研究		Textbooks. Textbook research
97U30	教师手册和计划辅助设备		Teachers’ manuals and planning aids
97U40	问题集.竞赛.考试		Problem books. Competitions. Examination
97U50	计算机辅助教学; e-学习		Computer assisted instruction; e-learning
97U60	操作材料		Manipulative materials
97U70	技术工具, 计算器		Technological tools, calculators
97U80	视听媒体		Audiovisual media
97U99	其它		None of the above, but in this section

146